7.41. Simulation and Fit of Vibronic Structure in Electronic Spectra, Resonance Raman Excitation Profiles and Spectra with the orca_asa Program¶
Deprecated since ORCA 6.0.0
The
orca_asaprogram is no longer supported. It is still included in the 6.0.0 release and the documentation is preserved below. However, it may not function correctly and will be removed in a future ORCA version!The
!NMScanand!NMGradkeywords are still available but these calculations may fail or not generate valid input fororca_asa. Please use the ESD module instead, if applicable.
In this section various aspects of the simulation and fit of optical
spectra, including absorption, fluorescence, and resonance Raman are
considered. This part of the ORCA is fairly autonomous and can also be
used in a data analysis context, not only in a “quantum chemistry” mode.
The program is called orca_asa, where ASA stands for
“Advanced Spectral
Analysis”. The program was entirely designed by Dr. Taras
Petrenko.
The general philosophy is as follows: An ORCA run produces the necessary
data to be fed into the orca_asa program and writes an initial input
file. This input file may be used to directly run orca_asa in order to
predict an absorption, fluorescence or resonance Raman spectrum.
Alternatively, the input file may be edited to change the parameters
used in the simulations. Last – but certainly not least – the
orca_asa program can be used to perform a fit of the model parameters
relative to experimental data.
All examples below are taken from [678], which must be cited if you perform any work with the orca_asa program!
7.41.1. General Description of the Program¶
The program input comprises the following information: (1) model and specification of the model parameters characterizing the electronic structure of a molecule, as well as lineshape factors; (2) spectral ranges and resolution for simulations; (3) specification of vibrational transitions for rR excitation profile and spectra generation; (4) certain algorithm-selecting options depending on the model; (5) fitting options.
All optional parameters (1)-(3) are given in the %sim block, and
fitting options are in the %fit block. The model parameters are
specified within various blocks that will be described below. The
program orca_asa is interfaced to ORCA and inherits its input style.
The input for orca_asa run can be also generated upon ORCA run.
The current implementation features so called “simple”, “independent mode, displaced harmonic oscillator” (IMDHO), and “independent mode, displaced harmonic oscillator with frequency alteration” (IMDHOFA) models.
7.41.2. Spectral Simulation Procedures: Input Structure and Model Parameters¶
7.41.2.1. Example: Simple Mode¶
This model represents the simplest approach which is conventionally used in analysis of absorption spectra. It neglects vibrational structure of electronic transitions and approximates each individual electronic band by a standard lineshape, typically a Gaussian, Lorentzian or mixed (Voigt) function. This model can only make sense if vibrational progressions are not resolved in electronic spectra. Upon this approximation the intensity of absorption spectrum depends on the energy of the incident photon (\(E_{L} )\), the electronic transition energy (\(E_{T} )\), the transition electric dipole moment (\(\mathrm{\mathbf{M} }\), evaluated at the ground-state equilibrium geometry). Lineshape factors are specified by homogeneous linewidth \(\Gamma\) and standard deviation parameter \(\sigma\) corresponding to Gaussian distribution of transition energies. The following example illustrates a simple input for simulation of absorption bandshapes using various intensity and lineshape parameters.
# example001.inp
#
# Input file to generate absorption spectrum consisting
# of 3 bands with different lineshape factors:
#
# 1. Lorentzian centered at 18000cm**-1 (damping factor Gamma= 100 cm**-1)
# 2. Gaussian centered at 20000cm**-1
# (standard deviation Sigma= 100 cm**-1)
# 3. Mixed Gaussian-Lorentzian band representing Voigt profile
# centered at 21000 cm**-1
%sim
Model Simple
# Spectral range for absorption simulation:
AbsRange 17000.0, 23000.0
# Number of points to simulate absorption spectrum:
NAbsPoints 2000
end
#---------------------------------------------------------------------------
# Transition Gamma Sigma Transition Dipole Moment (atomic unit)
# Energy (cm**-1) (cm**-1) (cm**-1) Mx My Mz
#---------------------------------------------------------------------------
$el_states
3 # number of electronic states
1 18000.0 100.00 0.0 1.0 0.0 0.0
2 20000.0 0.00 100.0 1.0 0.0 0.0
3 22000.0 50.00 50.0 1.0 0.0 0.0
The parameters of of the final electronic states reached by the
respective transitions are specified in the $el_states block. The
spectral range and resolution used in the calculation are defined by the
AbsRange and NAbsPoints keywords in %sim block. The calculation of
the absorption spectrum is automatically invoked if NAbsPoints>1.
After the orca_asa run you will find in your directory file
example001.abs.dat containing absorption spectrum in simple two-column
ASCII format suitable to be plotted with any spreadsheet program.
Absorption spectra corresponding to individual electronic transitions
are stored in file example001.abs.as.dat ( the suffix “as” stands
for “All States”).
Fig. 7.43 Absorption spectrum generated after orca_asa run on file
example001.inp. Three bands have different lineshape pararameters.
Note that although all transitions are characterized by the same
transition electric dipole moment their intensities are scaled
proportionally to the transition energies.¶
The output of the program run also contains information about oscillator strengths and full-width-half-maximum (FWHM) parameters corresponding to each electronic band:
----------------------------------------------
State EV fosc Stokes shift
(cm**-1) (cm**-1)
----------------------------------------------
1: 18000.00 0.054676 0.00
2: 20000.00 0.060751 0.00
3: 22000.00 0.066826 0.00
----------------------------------------
BROADENING PARAMETETRS (cm**-1)
----------------------------------------
State Gamma Sigma FWHM
----------------------------------------
1: 100.00 0.00 200.00
2: 0.00 100.00 235.48
3: 50.00 50.00 180.07
Note that although all three types of lineshape functions are symmetric this is not true for the overall shapes of individual absorption bands since the extinction coefficient (absorption cross-section) is also proportional to the incident photon energy. Therefore, if the linewidth is larger than 10% of the peak energy the asymmetry of the electronic band can be quite noticeable.
7.41.2.2. Example: Modelling of Absorption and Fluorescence Spectra within the IMDHO Model¶
The IMDHO model is the simplest approach that successfully allows for the prediction of vibrational structure in electronic spectra as well as rR intensities for a large variety of real systems. This model assumes:
harmonic ground- and excited-state potential energy surfaces;
origin shift of the excited-state potential energy surface relative to the ground-state one;
no vibrational frequency alteration or normal mode rotation occurs in the excited state;
no coordinate dependence of the electronic transition dipole moment.
In addition to the parameters that enter the “Simple model” defined above it requires some information about the vibrational degrees of freedom. The required information consists of the ground-state vibrational frequencies \(\left\{{ \omega_{gm} } \right\}\) and (dimensionless) origin shifts \(\left\{{ \Delta_{mi} } \right\}\), where \(i\) and \(m\) refer to electronic states and normal modes respectively. \(\Delta\) is expressed in terms of dimensionless normal coordinates. Accordingly, for the IMDHO model one has to specify the following blocks
The
$el_statesblock contains the parameters \(E_{T}, \Gamma, \sigma, \mathrm{\mathbf{M} }\) for each electronic state. By default \(E_{T}\) is assumed to be adiabatic minima separation energy. Alternatively, it can be redefined to denote for the vertical transition energy.This is achieved by specifiying the keywordEnInput=EVin the%simblock.A
$vib_freq_gsblock specifies ground-state vibrational frequencies.A
$sdncblock contains parameters \(\left\{{ \Delta_{mi} } \right\}\) in matrix form such that the \(i\)-th column represents the dimensionless displacements along all normal modes for the \(i\)-th excited-state PES.
The file example002.inp provides the input for simulation of
absorption and fluorescence spectra of a system characterized by
significant displacements of the excited-state origin along 5 normal
coordinates.
# example002.inp
#
# Input file for simulation of vibrational structure
# in absorption and fluorescence spectra assuming
# origin shift of excited PES along 5 normal coordinates.
# The simulated spectra closely reproduce the experimental
# optical bandshapes for the tetracene molecule.
#
%sim
Model IMDHO
# spectral range for absorption simulation (cm**-1)
AbsRange 20000.0, 27000.0
NAbsPoints 2000 # number of points in absorption spectrum
# spectral range for simulation of fluorescence (cm**-1)
FlRange 22000.0, 16000.0
NFlPoints 2000 # number of points in fluorescence spectrum
# the following options require the spectra to be normalized
# so that their maxima are equal to 1.0
AbsScaleMode Rel
FlScaleMode Rel # default for fluorescence
# for absorption spectrum the default option is AbsScaleMode= Ext
# which stands for extinction coefficient
end
#---------------------------------------------------------------------------
# Transition Gamma Sigma Transition Dipole Moment (atomic unit)
# Energy (cm**-1) (cm**-1) (cm**-1) Mx My Mz
#---------------------------------------------------------------------------
$el_states
1
1 21140.0 50.00 100.0 1.0 0.0 0.0
# Block specifying Stokes Shift parameter for each electronic state
# This information is optional
$ss
1 # number of excited states
1 300.0 # the Stokes shift for the 1st electronic transition
# Block providing the values of VIBrational FREQuencies
# for 5 Ground-State normal modes.
# Obligatory for IMDHO and IMDHOFA models.
$vib_freq_gs
5
1 310.0
2 1193.0
3 1386.0
4 1500.0
5 1530.0
# Block specifying origin Shift of the excite-state PES
# along each normal mode in terms of the ground-state
# Dimensionless Normal Coordinates
# Obligatory for IMDHO and IMDHOFA models.
$sdnc
5 1
1
1 0.698
2 -0.574
3 0.932
4 -0.692
5 0.561
The calculation of absorption and fluorescence spectra is automatically
invoked if the parameters NAbsPoints>1 and NFlPoints> 1. The input
file also contains the optional block $ss which specifies the Stokes
shift \(\lambda\) for each electronic transition. This parameter is equal
to the energy separation between the 0-0 vibrational peaks in the
absorption and fluorescence spectra as shown in Fig. 7.44 . In general
\(\lambda\) accounts for solvent induced effects as well as unresolved
vibrational structure corresponding to low-frequency modes that are not
specified in the input. Note that we have specified parameters
AbsScaleMode=Rel and FlScaleMode=Rel in %sim block in order to
ensure that the simulated spectra are normalized to unity. The
calculated absorption and fluorescence spectra are stored in
example002.abs.dat and example002.fl.dat files, respectively.
Fig. 7.44 Absorption and fluorescence spectra generated after orca_asa run on
the file example002.inp. If the homogeneous broadening is set to be
\(\Gamma = 10 \, \text{cm}^{-1}\) one can resolve underlying vibrational
structure and identify various fundamental and combination
transitions.¶
7.41.2.3. Example: Modelling of Absorption and Fluorescence Spectra within the IMDHOFA Model¶
IMDHOFA (Independent Mode Displaced Harmonic Oscillators with Frequency
Alteration) is based on the same assumptions as the IMDHO model except
for vibrational frequency alteration in excited state can take place.
The file example003.inp features almost the same input parameters as
example002.inp. The IMDHOFA model is invoked by the keyword
Model=IMDHOFA in the %sim block. Additionally, one has to provide
the obligatory block $vib_freq_es. It contains the excited-state
vibrational frequencies \(\left\{{ \omega_{emi} } \right\}\) in matrix
form such that the \(i\)-th column represents the vibrational frequencies
of all normal modes for the \(i\)-th excited-state PES.
# Block providing the values of VIBrational FREQuencies
# for 5 Excited-State normal modes.
# Obligatory for IMDHOFA model.
$vib_freq_es
5 1 # number of modes and number of excited states
1
1 410.0
2 1293.0
3 1400.0
4 1600.0
5 1730.0
Fig. 7.45 Absorption and fluorescence spectra generated after orca_asa run on
the file example003.inp. Also, the high-resolution spectra
corresponding to homogeneous broadening \(\Gamma = 10 \, \text{cm}^{-1}\)
are shown.¶
7.41.2.4. Example: Modelling of Effective Broadening, Effective Stokes Shift and Temperature Effects in Absorption and Fluorescence Spectra within the IMDHO Model¶
For the IMDHO model the orca_asa is capable to model absorption and
emission spectra in the finite-temperature approximation. While the
keyword Model=IMDHO assumes the zero-temperature approximation, the
value of Model=IMDHOT invokes the calculation of the spectra for the
finite temperature which is specified by the paramter TK in the block
%sim:
# example004.inp
#
#
%sim
Model IMDHOT
TK 300 # temperature (in Kelvin)
# spectral range for absorption simulation (cm**-1)
AbsRange 18000.0, 35000.0
NAbsPoints 5000 # number of points in absorption spectrum
# spectral range for simulation of fluorescence (cm**-1)
FlRange 22000.0, 10000.0
NFlPoints 5000 # number of points in fluorescence spectrum
# the following options require the spectra to be normalized
# so that their maxima are equal to 1.0
AbsScaleMode Rel
FlScaleMode Rel # default for fluorescence
end
#---------------------------------------------------------------------------
# Transition Gamma Sigma Transition Dipole Moment (atomic unit)
# Energy (cm**-1) (cm**-1) (cm**-1) Mx My Mz
#---------------------------------------------------------------------------
$el_states
1
1 21140.0 50.00 100.0 1.0 0.0 0.0
# Block specifying Stokes Shift parameter for each electronic state
$ss
1 # number of excited states
1 300.0 # the Stokes shift for the 1st electronic transition
# Block providing the values of VIBrational FREQuencies
# for 10 Ground-State normal modes.
$vib_freq_gs
10
1 30.0
2 80.0
3 100.0
4 120.0
5 130.0
6 140.0
7 160.0
8 200.0
9 310.0
10 1300.0
# Block specifying origin Shift of the excite-state PES
# along each normal mode in terms of the ground-state
# Dimensionless Normal Coordinates
$sdnc
10 1
1
1 2.5
2 2.0
3 1.8
4 1.9
5 1.5
6 1.9
7 2.4
8 1.9
9 2.5
10 0.9
This example illustrates a typical situation in large molecules which feature a number of low frequency modes with significant values of dimensionless displacements for a given excited-state PES. In the case of high density of vibrational states with frequencies below or comparable to the intrincic value of FWHM (determined by \(\Gamma\) and \(\sigma\)) the vibrational progression is unresolved, whereby the spectra become very diffuse and show large separation between the maxima of absorption and emission spectra (Fig. 7.45). Besides, upon the condition \(h\nu_{i} \leqslant kT\) the effective bandwidths and positions of maxima in the spectra can be strongly subject to temperature effects.
Fig. 7.46 Absorption and fluorescence spectra for T\(=\)0 K
(blue) and T\(=\)300 K (red) generated after orca_asa
run on the file example004.inp. Black lines show spectra corresponding
to the case where all low-frequency modes were excluded from the
calculation.¶
The effective Stokes shift and linewidth parameters which are evaluated
in the simple self-consistent procedure are given in the output of the
orca_asa run:
------------------------------------------------------------------------------
State E0 EV fosc Stokes shift Effective Stokes shift
(cm**-1) (cm**-1) (cm**-1) (cm**-1)
------------------------------------------------------------------------------
1: 21140.00 24535.85 0.074529 300.00 7091.70
-----------------------------------------------------------------------------------------------
BROADENING PARAMETETRS (cm**-1)
-----------------------------------------------------------------------------------------------
Intrinsic Effective
State -------------------------- --------------------------------------------------------
Sigma FWHM
Gamma Sigma FWHM --------------------------- ---------------------------
0K 298.15K 300.00K 0K 298.15K 300.00K
-----------------------------------------------------------------------------------------------
1: 50.00 100.00 293.50 1125.34 1411.13 1413.57 2703.84 3376.75 3382.48
Note that the evaluation of the effective parameters is rather approximate and these values can noticeable deviate from those which can be directly deduced from the calculated spectra. However, such an information usually provides the proper order of magnitude of the effective vibronic broadening and Stokes shift. As indicated in the program output above, the effective bandshape has predominantly a Gaussian character which varies with the temperature so that \(\sigma = 1125 \, \text{cm}^{-1}\) (\(T = 0\) K) and \(\sigma =1414 \, \text{cm}^{-1}\) (\(T=300\) K). Indeed, as shown in Fig. 7.47 the absorption spectrum at \(T=300\) K can be well fitted using Gaussian lineshape with \(\sigma = 1388 \, \text{cm}^{-1}\) (FWHM\(= 3270 \, \text{cm}^{-1}\)). One can see that at higher temperatures the deviation between the spectrum and its Gauss fit becomes even smaller.
In molecules the normal distribution of the electronic transition energies in the ensemble would give rise to a Gaussian bandshape of the absorption band. However, the corresponding standard deviation is expected to be of the order of 100 cm\(^{-1}\), whereby a typical Gaussian bandwidth of the order of 1000 cm\(^{-1}\) appears to result from unresolved vibronic progression. In general, this statement is supported by quantum chemical calculation of the model parameters. In principle the effective bandwidth parameters can also be used for characterization and assignement of individual electronic bands.
Fig. 7.47 Absorption spectrum (blue) for \(T=300\) K generated after orca_asa
run on the file example004.inp. Red line represents the Gauss-fit of
the calculated spectrum.¶
7.41.2.5. Example: Modelling of Absorption and Resonance Raman Spectra for the 1-\(^1\)A\(_g\) \(\rightarrow\) 1-\(^1\)B\(_u\) Transition in trans-1,3,5-Hexatriene¶
The hexatriene molecule is characterized by 9 totally-symmetric normal modes which dominate vibrational structure in absorption and are active in rR spectra corresponding to the strongly dipole-allowed \(1-^{1}A_{g} \rightarrow 1-^{1}B_{u}\) transition around 40000 cm\(^{-1}\) . Except for some peculiarities related to the neglect of normal mode rotations in the excited state the optical spectra are quite satisfactorily described by the IMDHO model.
The following input exemplifies simulation of absorption spectrum and rR spectra for an arbitrary predefined number of excitation energies.
#
# example005.inp
#
# input for simulation of absorption and resonance Raman spectra
# using experimental values of transition energy and displacement
# parameters corresponding to the strongly allowed 1-1Ag 1-1Bu transition
# in trans-1,3,5-hexatriene
#
%sim
Model IMDHO
AbsRange 38000.0, 48000.0
NAbsPoints 2000
AbsScaleMode Rel
# resonance Raman intensities will be calculated
# for all vibrational states with excitation number
# up to RamanOrder:
RamanOrder 4
# excitation energies (cm**-1) for which rR spectra will be calculated:
RRSE 39500, 39800, 41400
# full width half maximum of Raman bands in rR spectra (cm**-1):
RRS_FWHM 10
RSRange 0, 5000 # spectral range for simulation of rR spectra (cm**-1)
NRRSPoints 5000 # number of points to simulate rR spectra (cm**-1)
end
$el_states
1
1 39800.0 150.00 0.0 1.0 0.0 0.0
$vib_freq_gs
9
1 354.0
2 444.0
3 934.0
4 1192.0
5 1290.0
6 1305.0
7 1403.0
8 1581.0
9 1635.0
$sdnc
9 1
1
1 0.55
2 0.23
3 0.23
4 0.82
5 0.485
6 0.00
7 0.085
8 0.38
9 1.32
After the orca_asa run the following files will be created:
example005abs.datcontains the simulated absorption spectrum. It is shown in Fig. 7.48.example005.o4.rrs.39500.dat,example005.o4.rrs.39800.datandexample005.o4.rrs.41400.datcontain the simulated rR spectra for excitation energies at 39500, 39800 and 41400 cm\(^{-1}\), respectively. The suffix “o4” stands for the order of Raman scattering specified in the input by keywordRamanOrder=4. The rR specta are shown in Fig. 7.49.example005.o4.rrs.39500.stk,example005.o4.rrs.39800.stkandexample005.o4.rrs.41400.stkprovide Raman shifts and intensities for each vibrational transition. Corresponding vibrational states are specified by the quantum numbers of excited modes.
Fig. 7.48 Absorption spectrum corresponding to
\(1-^{1}A_{g} \rightarrow 1-^{1}B_{u}\) transition in
trans-1,3,5-hexatriene generated after orca_asa run on the file
example005.inp.¶
Fig. 7.49 Resonance Raman spectra for 3 different excitation energies which fall in resonance with \(1-^{1}A_{g} \rightarrow 1-^{1}B_{u}\) transition in trans-1,3,5-hexatriene.¶
NOTE
By default the program provides rR spectra on an arbitrary scale since only relative rR intensities within a single rR spectrum are of major concern in most practical cases. However, one can put rR spectra corresponding to different excitation energies on the same intensity scale by providing the keyword
RSISM=ASRin%simblock (RSISM – Raman Spectra Intensity Scaling Mode; ASR – All Spectra Relative). By defaultRSISM=SSR(SSR – Single Spectrum Relative) for which each rR spectrum is normalized so that the most intense band in it has intensity 1.0. The relative intensities of bands in rR spectra measured for different excitation energies can be compared if they are appropriately normalized relative to the intensity of a reference signal (e.g. Raman band of the solvent). We also keep in mind the possibility to extend our methodology in order to provide the absolute measure of rR intensities in terms of the full or differential cross-sections.Within the harmonic model, for a single electronic state neither relative rR intensities nor absorption bandshapes in the case of
AbsScaleMode=Reldo depend on the values of the electronic transition dipole moment (unless it is precisely zero).
In the example above resonance Raman spectra have been generated for all
vibrational transitions with total excitation number up to the value
specified by the parameter RamanOrder. Its is also possible to make
explicit specification of vibrational states corresponding to various
fundamental, overtone and combination bands via the $rr_vib_states
block. In such a case rR spectra involving only these vibrational
transitions will be generated separately.
$rr_vib_states 5 # total number of vibrational transitions
1
modes 1
quanta 1; # final vibrational state for the fundamental band corresponding to mode 1
2
modes 9
quanta 1; # final vibrational state for the fundamental band corresponding to mode 9
3
modes 3, 4
quanta 1, 1; # final vibrational state for the combination band involving single
# excitations in modes 3 and 4
4
modes 5
quanta 3; # final vibrational state for the second overtone band corresponding to
# mode 5
5
modes 1, 5,9
quanta 1,2, 1; # final vibrational state for the combination band involving single
# excitations in modes 1 and 2, and double excitation in mode 5
Each vibrational transition is specified via the subblock which has the following structure:
k
modes m1,m2,...mn
quanta q1,q2,...qn;
This means that the \(k\)-th transition is characteriezed by excitation numbers \(q_{i}\) for modes \(m_{i}\) so that corresponding Raman shift is equal to \(\nu =\sum\nolimits{ q_{i} \nu_{i} }\), where \(\nu_{i}\) is vibrational frequency of the mode \(m_{i}\).
After the orca_asa run the following files will be created in
addition:
example005.us.rrs.39500.dat,example005.us.rrs.39800.datandexample005.us.rrs.41400.datcontain the simulated rR spectra involving only vibrational transitions specified in the$rr_vib_statesblock, for excitations energies at 39500, 39800 and 41400 cm\(^{-1}\), respectively. The suffix “us” stands for “User specified vibrational States”.example005.us.rrs.39500.stk,example005.us.rrs.39800.stkandexample005.us.rrs.41400.stkprovide Raman shifts and intensities for each vibrational transition specified in the$rr_vib_statesblock.
7.41.2.6. Example: Modelling of Absorption Spectrum and Resonance Raman Profiles for the 1-\(^1\)A\(_g\) \(\rightarrow\) 1-\(^1\)B\(_u\) Transition in trans-1,3,5-Hexatriene¶
The following example illustrates an input for simulation of absorption bandshape and resonance Raman profiles (RRP):
#
# example006.inp
#
# input for simulation of absorption and resonance Raman profiles
# using experimental values of transition energy and displacement
# parameters corresponding to the strongly allowed 1-1Ag 1-1Bu transition
# in trans-1,3,5-hexatriene
#
%sim
Model IMDHO
AbsRange 38000.0, 48000.0
NAbsPoints 2000
AbsScaleMode Rel
RRPRange 38000.0, 48000.0 # spectral range for simulation of
# rR profiles (cm**-1)
NRRPPoints 2000 # number of points for simulation of rR profiles
CAR 0.8
RamanOrder 2
end
$el_states
1
1 39800.0 150.00 0.0 1.0 0.0 0.0
$vib_freq_gs
9
1 354.000000
2 444.000000
3 934.000000
4 1192.000000
5 1290.000000
6 1305.000000
7 1403.000000
8 1581.000000
9 1635.000000
$sdnc
9 1
1
1 0.55
2 0.23
3 0.23
4 0.82
5 0.485
6 0.00
7 0.085
8 0.38
9 1.32
$rr_vib_states 5 # total number of vibrational transitions
1
modes 1
quanta 1;
2
modes 9
quanta 1;
3
modes 3, 4
quanta 1, 1;
4
modes 5
quanta 3;
5
modes 1, 5,9
quanta 1,2, 1;
The keyword RamanOrder=2 will invoke generation of rR profiles for all
vibrational transitions with total excitation number up to 2 in the
range of excitation energies specified by the keywords RRPRange and
NRRPPoints. Likewise, rR profiles for the vibrational states given in
the $rr_vib_states block will be generated separately. Since in most
cases only relative rR intensities are important, and one would be
interested to compare absorption bandshape and shapes of individual rR
profiles, the keyword CAR = 0.8 is used to scale rR profiles for all
vibrational transitions by a common factor in such a way that the ratio
of the maximum of all rR intensities and the maximum of absorption band
is equal to 0.8.
After the orca_asa run the following files will be created:
example006.abs.datcontains the simulated absorption spectrum (Fig. 7.50).example006.o1.rrp.datandexample006.o2.rrp.datcontain rR profiles for vibrational transitions with total excitation numbers 1 and 2, respectively. RR profiles for all fundamental bands (from the fileexample006.o1.rrp.dat) are shown in Fig. 7.50.example006.o1.infoandexample006.o1.infocontain specification of vibrational transitions with total excitation numbers 1 and 2, respectively, as well as corresponding Raman shifts.example006.us.rrp.1.dat–example006.us.rrp.5.dat contain rR profiles for vibrational transitions 1–5 specified in the$rr_vib_statesblock.
Fig. 7.50 Absorption spectrum and resonance Raman profiles of fundamental bands corresponding to \(1-^1A_g \rightarrow 1-^1B_u\) transition in trans-1,3,5-hexatriene.¶
7.41.3. Fitting of Experimental Spectra¶
7.41.3.1. Example: Gauss-Fit of Absorption Spectrum¶
An absorption spectrum basically consists of a number of absorption
bands. Each absorption band corresponds to a transition of the ground
electronic state to an excited electronic state. In molecules such
transitions are usually considerably broadened. In many cases there will
be overlapping bands and one would need to deconvolute the broad
absorption envelope into contributions from individual transitions.
Within the “Simple model” the orca_asa program enables fit of an
absorption spectrum with a sum of standard lineshape functions
(Gaussian, Lorentzian) or more general Voigt functions. In most cases,
one simply performs a “Gauss-Fit”. That is, it is assumed that the shape
of each individual band is that of a Gaussian function. Then one applies
as many (or as few) Gaussians as are necessary for an accurate
representation of the absorption envelope. In order to explain the
fitting procedures within the “Simple model” let us consider an
experimental absorption spectrum in
Fig. 7.51:
Fig. 7.51 Experimental absorption spectrum. Bars indicate transition energies which were used for the initial guess in the input for spectral fitting.¶
As shown in Fig. 7.51 one can identify roughly 7 electronic bands. The
initial estimates of transition energies corresponding to the maxima and
shoulders in the absorption spectrum (indicated by bars in
Fig. 7.51) and
rather approximate values of inhomogeneous broadening and transition
dipole moment components are specified in the $el_states block of the
input file for the spectral fitting:
# example007.inp
#
# Input file for fitting of experimental absorption spectrum
#
%sim
model Simple
end
%fit
Fit true # Global flag to turn on the fit
AbsFit true # Flag to include absorption into the fit
method Simplex
WeightsAdjust true
AbsRange 0.0, 100000.0 # absorption spectral range to be included in the fit;
# in the present case all experimental points
# will be included
AbsName "absexp.dat" # name of the file containing experimental
# absorption spectrum in a simple two-column
# ASCII format
ExpAbsScaleMode Ext # This keyword indicates that the experimental
# absorption intensity is given in terms of
# the extinction coefficient. This is important
# for the proper fitting of transition dipole
# moments and oscillator strengths
NMaxFunc 10000 # maximum number of function evaluations in simplex
# algorithm
MWADRelTol 1e-5 # Relative Tolerance of the Mean Weighted Absolute
# Difference (MWAD) function which specifies the
# convergence criterion
E0Step 500.00 # initial step for the transition energies
# in the simplex fitting
TMStep 0.5 # initial step for the transition dipole moments
# in the simplex fitting
E0SDStep 500.0 # initial step for the inhomogeneous linewidth (Sigma)
# in the simplex fitting
end
# ! Parameters specified in the $el_states block
# are used as initial guess in the fit
#---------------------------------------------------------------------------
# Transition Gamma Sigma Transition Dipole Moment (atomic unit)
# Energy (cm**-1) (cm**-1) (cm**-1) Mx My Mz
#---------------------------------------------------------------------------
$el_states
7
1 11270 0.0 1000.00 1.0000 0.0000 0.0000
2 15100 0.0 1000.00 1.0000 0.0000 0.0000
3 20230 0.0 1000.00 1.0000 0.0000 0.0000
4 27500 0.0 1000.00 1.0000 0.0000 0.0000
5 31550 0.0 1000.00 1.0000 0.0000 0.0000
6 37070 0.0 1000.00 1.0000 0.0000 0.0000
7 39800 0.0 1000.00 1.0000 0.0000 0.0000
# the integer values specified in $el_states_c block indicate parameters
# in the $el_states block to be varied
$el_states_c
7
1 1 0 1 1 0 0
2 2 0 2 2 0 0
3 3 0 3 3 0 0
4 4 0 4 4 0 0
5 5 0 5 5 0 0
6 6 0 6 6 0 0
7 7 0 7 7 0 0
The functionality of the constraint block $el_states_c should be
understood as follows: 1) 0 flag indicates that the corresponding
parameter in the $el_state block will not be varied in the fitting; 2)
if the number corresponding to a certain parameter coincides with the
number of the corresponding electronic state this parameter will be
varied independently. Thus, the block $el_states_c in the input
indicates that all transition energies, inhomogeneous linewidths and
x-components of the transition electric dipole moment will be varied
independently, while homogeneous linewidths, y- and z-components of the
transition dipole moment will be fixed to their initial values.
The following considerations are important:
Since in conventional absorption spectroscopy one deals with the orientationally averaged absorption cross-section, the signal intensity is proportional to the square of the transition electric dipole moment \(\left|{ \mathrm{\mathbf{M} }} \right|^{2}\). Thus, the intensities do not depend on the values of the individual components of \(\mathrm{\mathbf{M} }\) as long as \(\left|{ \mathrm{\mathbf{M} }} \right|^{2}= \text{const}\). Therefore, we have allowed to vary only \(M_{x}\) components. Otherwise there can be problems in convergence of the fitting algorithm.
The sum of the weights of experimental points which enter the mean absolute difference function employed in the minimization is always kept equal to the number of experimental points. In the case of equidistant experimental photon energies all weights are assumed to be equal. However, in experimental electronic spectra the density of spectral points can increase significantly upon going from high- to low-energy spectral regions, which is due to the fact that experimental absorption spectra are initially acquired on the wavelength scale. In such a case the quality of the fit can be noticeably biased towards low-energy spectral region. Therefore, it is advisable to adjust relative weights of experimental points according to the their density which is controlled by the keyword
WeightsAdjustin the%fitblock. Although this parameter is not crucial for the present example, in general, it will provide a more balanced fit.The parameters
E0Step,TMStep,E0SDStepin the%fitblock specify the initial dimension of the simplex in the space of \(E_{T} ,\mathrm{\mathbf{M} }, \sigma\) and should roughly correspond to the expected uncertainty of initial guess on these parameters in the$el_statesblock relative to their actual values. The quality of the fit can noticeably deteriorate if the parameters specifying initial steps are too low or too high.
The fit run of orca_asa on file example007.inp will converge upon
approximately 3600 function evaluations (for MWADRelTol=1e-5). The
results of the fit will be stored in file example007.001.inp which has
the same structure as the input file example007.inp. Thus, if the fit
is not satisfactory and/or it is not fully converged it can be refined
in a subsequent orca_asa run upon which file example007.002.inp will
be created, and so on. Some model parameters in intermediate files can
be be additionally modified and/or some constraints can be lifted or
imposed if so desired. The output file example007.001.inp will contain
fitted model parameters stored in the $el_states block:
$el_states
7
1 11368.24 0.00 732.50 1.6290 0.0000 0.0000
2 15262.33 0.00 495.17 -0.2815 0.0000 0.0000
3 19500.08 0.00 1023.39 0.2300 0.0000 0.0000
4 26969.01 0.00 1832.30 1.4089 0.0000 0.0000
5 31580.41 0.00 1440.87 1.8610 0.0000 0.0000
6 35769.07 0.00 1804.02 1.5525 0.0000 0.0000
7 39975.11 0.00 1909.38 2.4745 0.0000 0.0000
The overall quality of the fit is determined by the parameter MWAD which upon convergence reaches the value of \(\approx\)0.009 (MWAD stands for Mean Weighted Absolute Difference).
After the orca_asa run files absexp.fit.dat and absexp.fit.as.dat
will be created. Both files contain the experimental and fitted spectra
which are shown in Fig. 7.52 . In addition, the file absexp.fit.as.dat will
contain individual contributions to the absorption spectrum
corresponding to different excited states.
Fig. 7.52 Comparison of the experimental (black curve) and fitted (red)
absorption spectra corresponding to the fit run of orca_asa on the
file example007.inp. Blue curves represent individual contributions to
the absorption spectrum from each state.¶
Since there is a noticeable discrepancy between the fitted and
experimental spectra around 13000 cm\(^{-1}\) (Fig. 7.52) it is
worthwhile to refine the fit after adding parameters for a new state in
the file example007.001.inp:
$el_states
8
1 11368.24 0.00 732.50 1.6290 0.0000 0.0000
... ... ...
8 13280.00 0.00 1000.00 1.000 0.0000 0.0000
$el_states_c
8
1 1 0 1 1 0 0
... ... ...
8 8 0 8 8 0 0
Actually, the character of the discrepancy in the present case is very similar to that in Fig. 7.49 (section Example: Modelling of Effective Broadening, Effective Stokes Shift and Temperature Effects in Absorption and Fluorescence Spectra within the IMDHO Model) where a vibronically broadened absorption spectrum was fitted with a Gaussian lineshape. Thus, the poor fit in the region around 1300 cm\(^{-1}\) is most likely due to the essentially asymmetric character of the vibronic broadening rather than to the presence of another electronic band.
As shown in Fig. 7.53 the refined fit leads to much better agreement between the experimental and fitted absorption spectra (MWAD\(=\)0.0045).
Fig. 7.53 Comparison of the experimental (black) and fitted (red) absorption
spectra corresponding to the fit run of orca_asa on the file
example007.001.inp. Blue curves represent individual contributions to
the absorption spectrum from each state.¶
Due to some peculiarities of the simplex algorithm for function
minimization, you can still refine the fit by rerunning orca_asa on
the file example007.002.inp! This leads to an even lower value of the
parameter MWAD\(=\) 0.0038, and therefore to better agreement of
experimental and fitted spectra (even though the previous run has been
claimed to be converged).
It is also possible to perform a fit using the same value of
inhomogeneous linewidth for all electronic states. For this purpose one
needs to choose as a guess the same linewidth parameters in the
$el_states block:
$el_states
8
1 11118.58 0.00 1000.0 1.0687 0.0000 0.0000
2 13673.38 0.00 1000.0 -0.5530 0.0000 0.0000
3 21267.40 0.00 1000.0 0.3675 0.0000 0.0000
4 27024.71 0.00 1000.0 1.4041 0.0000 0.0000
5 31414.74 0.00 1000.0 1.7279 0.0000 0.0000
6 35180.77 0.00 1000.0 1.6246 0.0000 0.0000
7 39985.52 0.00 1000.0 2.5708 0.0000 0.0000
8 11665.01 0.00 1000.0 1.2332 0.0000 0.0000
In addition the constraint block should be modified as follows:
$el_states_c
8
1 1 0 1 1 0 0
2 2 0 1 2 0 0
3 3 0 1 3 0 0
4 4 0 1 4 0 0
5 5 0 1 5 0 0
6 6 0 1 6 0 0
7 7 0 1 7 0 0
8 8 0 1 8 0 0
The constraint parameters for the inhomogeneous broadening were chosen to be 1, which means that formally \(\sigma_{1}\) corresponding to the first state is varied independently while the linewidths \(\left\{{ \sigma_{i} } \right\}\) for other bands are varied in such a way that the ratios \(\sigma _{i} /\sigma_{1}\) are kept fixed to their initial values, whereby the same linewidth parameter will be used for all states.
Fig. 7.54 Comparison of the experimental (black) and fitted (red) absorption
spectra corresponding to the fit run of orca_asa on the file
example007.002.inp in which equal broadening was assumed for all
electronic bands. Blue curves represent individual contributions to the
absorption spectrum from each state.¶
One can see (Fig. 7.54) that the assumption of equal linewidths for all electronic bands leads to a rather pronounced deterioration of the quality of the fit in the low-energy spectral range (MWAD\(=\)0.017). Apparently, this discrepancy can be fixed assuming more electronic states at higher energies.
NOTE
The homogeneous linewidth parameters can also be included in the fit in a similar way. However, one can see that in most cases they appear to be much smaller than corresponding Gaussian linewidth parameters.
Gauss-fit of absorption spectra is coventionally performed assuming the same linewidth parameters for all bands. However, since a large portion of Gaussian broadening is mainly due to the unresolved vibronic structure in the spectra which can significantly vary depending on the nature of transition, the assumption of unequal Gaussian bandwidths seems to be a physical one.
7.41.3.2. Example: Fit of Absorption and Resonance Raman Spectra for 1-\(^1\)A\(_g\) \(\rightarrow\) 1-\(^1\)B\(_u\) Transition in trans-1,3,5-Hexatriene¶
Below we provide an example of the fit of the lineshape parameters and
\(\left\{{\Delta_{m} } \right\}\) corresponding to the strongly
dipole-allowed 1-\(^{1}\)A\(_{g}\)
\(\rightarrow\)1-\(^{1}\)B\(_{u}\) transition in hexatriene.
It is known that the most intense bands in rR spectra correspond to the
most vibronically active in absorption spectrum. For the IMDHO model
this correlation is determined by the values of \(\left\{{ \Delta_{m} }
\right\}\). Thus, the larger \(\Delta\), the larger is the rR intensity of
a given mode and the more pronounced is the progression in the
absorption spectrum corresponding to this mode. In principle, if all
vibrational transitions in absorption are well resolved it is possible
to determine \(\left\{{ \Delta
_{m} } \right\}\) by a fit of the absorption spectrum alone. In practice
this task is ambiguous due to the limited resolution of the experimental
absorption spectra. The observation of a rR spectrum enables the
identification of the vibrational modes that are responsible for the
progression in the absorption spectrum, as well as a quantitative
analysis in terms of \(\left\{{ \Delta_{m} } \right\}\). The file
example006.inp provides a brute-force example on how to approach the
fit employing the minimal possible experimental information: 1) An
absorption spectrum; 2) relative rR intensities of fundamental bands for
a given excitation energy. The rR spectrum upon the excitation in
resonance with the 0-0 vibronic band at 39809 cm\(^{-1}\) is shown in
Fig. 7.43.
Fig. 7.55 Experimental Resonance Raman spectrum corresponding to 1-\(^1\)A\(_g\) \(\rightarrow\) 1-\(^1\)B\(_u\) transition in trans-1,3,5-hexatriene.¶
The experimental rR spectrum has enabled the identification of seven vibrational modes that give rise to the most intense resonance Raman bands. Therefore, they are expected to have the largest excited-state displacements and the most pronounced effect on the vibrational structure of the absorption spectrum. Their vibrational frequencies have been entered as input for the fit as shown below:
#
# example008.inp
#
# Input for fit of absorption and resonance Raman spectra
# corresponding to the strongly allowed 1-1Ag 1-1Bu transition
# in 1,3,5 trans-hexatriene.
#
# Parameters to be varied:
# 1) adiabatic minima transiton energy
# 2) homogeneous linewidth (Gamma)
# 3) dimensionless normal coordinate displacements of the
# excited-state origin
#
%sim
Model IMDHO
end
%fit
Fit true # boolean parameter to switch on the fit
# boolean parameter to include experimental absorption
# spectrum in the fit:
AbsFit true
# boolean parameter to include experimental rR spectra
# specified in $rrs_exp block in the fit:
RRSFit true
AbsExpName "hex-abs.dat" # name of the file with experimental absorption
# spectrum
# the following value of keyword ExpAbsScaleMode
# indicates that only the shape of absorption band
# but not its total intensity will be accounted in the fit:
ExpAbsScaleMode Rel
# the weight of absorption relative to the total weight of
# rR intensities in the difference function to be minimized:
CWAR 5.0
NMaxFunc 1000 # maximum number of function evaluations in simplex
# algorithm
MWADRelTol 1e-4 # Relative Tolerance of the Mean Weighted Absolute
# Difference (MWAD) function which specifies the
# convergence criterion
SDNCStep 1.0
end
# The values specified in $el_states block serve as initial guess in the fit
$el_states
1
1 40000.0 200.00 0.0 1.0 0.0 0.0
# the integer values specified in $el_states_c block indicate parameters
# in $el_states block to be varied
$el_states_c
1
1 1 1 0 0 0 0
# 7 totally symmetric vibrations which give rise to the most
# intense bands in the rR spectra are included into analysis.
# Experimental values of vibration frequencies are given:
$vib_freq_gs
7
1 354.0
2 444.0
3 934.0
4 1192.0
5 1290.0
6 1403.0
7 1635.0
# Initial guess for the values of dimensionless normal
# coordinate displacements of the excited-state origin
$sdnc
7 1
1
1 0.0
2 0.0
3 0.0
4 0.0
5 0.0
6 0.0
7 0.0
# the integer values specified in $sdnc_c block indicate parameters
# in $sdnc block to be varied
$sdnc_c
7 1
1
1 1
2 2
3 3
4 4
5 5
6 6
7 7
# specification of vibrational transitions and their intensities
# in experimental rR spectra:
$rrs_exp
1 # number of rR spectra
1 1 # start of the block specifying the 1st rR spectrum
Ex 39809.0 # excitation energy for the first rR spectrum
NTr 7 # number of vibrational transitions for which intensities are
# provided
1
int 10.0 1.0
modes 1
quanta 1;
2
int 5.0 1.0
modes 2
quanta 1;
3
int 1.5 1.0
modes 3
quanta 1;
4
int 21.0 1.0
modes 4
quanta 1;
5
int 7.5 1.0
modes 5
quanta 1;
6
int 2.0 1.0
modes 6
quanta 1;
7
int 46.0 1.0
modes 7
quanta 1;
The input of rR intensities for an arbitrary number of excitation
energies follows the keyword $rrs_exp block:
$rrs_exp
1 # number of rR spectra
1 1
The first “1” in the last line denotes the number of the rR spectrum for which specification starts below. If the second number is the same as the number of the spectrum, then it means that only relative intensities for the first rR spectrum are meaningful in the fit. If several spectra are given in the input then the second number may have a different value, e.g.:
$rrs_exp
3 # number of rR spectra
1 2
...
This input is to be interpreted as indicating that 3 rR spectra are provided and the relative intensities for the first spectrum are given on the same scale as the second one that will be accounted for in the fit. The value of the excitation energies and the number of vibrational transitions specified are indispensable within the blocks specifying intensities for each rR spectrum.
Following the number of vibrational transitions given by the keyword
NTr one has to specify each vibrational transition and its intensity.
Thus, in the present case there are seven subblocks with the following
structure:
k int I W
modes m1,m2,...mn
quanta q1,q2,...qn;
This means that the \(k\)-th transition has intensity \(I\) and weight \(W\) in the mean absolute difference function that is used for the minimization (\(W\) is an optional parameter). The following 2 lines specify the vibrational transitions by providing excitation numbers \(q_{i}\) for modes \(m_{i}\) so that the corresponding Raman shift is equal to \(\nu =\sum\limits_ { q_{i} \nu _{i} }\), where \(\nu_{i}\) is vibrational frequency of the mode \(m_{i}\).
The parameters that are to be varied are specified within the constraint
blocks $el_states_c and $sdnc_c. Both blocks have the same structure
and number of parameters as $el_states and $sdnc, respectively. A
parameter from the $el_states block is supposed to be independently
varied if its counterpart from the $el_states_c block is equal to the
number of the electronic state. Likewise, a parameter from the $sdnc
block is supposed to be independently varied if its counterpart from the
$sdnc_c block is equal to the number of the normal mode. Model
parameters that are set to 0 in the corresponding constraint blocks are
not varied in the fit. The values of the following parameters may be
important for the quality of the fit:
CWARin the%fitblock specifies the weight of absorption relative to the weight of rR intensities in the difference function to be minimized. If this parameter was not specified the fit would be almost insensitive to the rR intensities in the input, since typically the number of experimental absorption points is much larger than the number of rR transitions in the input. In most cases the value ofCWARin the range 1.0–5.0 is a good choice since the error in the measured experimental intensity is expected to be much smaller for absorption than for resonance Raman.SDNCStepin the%fitblock specifies the initial dimension of the simplex in the space of \(\left\{{ \Delta_{m} } \right\}\) and should roughly correspond to the expected uncertainty of initial guess on \(\left\{{ \Delta_{m} } \right\}\) in the$sdncblock compared to their actual values. You can notice in the present example that if this parameter is too large (>2.0) or too small (<0.4) the quality of the fit may significantly deteriorateAlthough the default initial dimensions of the simplex have reasonable values for different types of parameters it may turn out to be helpful in some cases to modify the default values:
FREQGStep 10.0 # ground-state vibrational frequencies
FREQEStep 10.0 # excited-state vibrational frequencies
E0Step 300.0 # transition energies
SSStep 20.0 # Stokes shift
TMStep 0.5 # electronic transition dipole moment
GammaStep 50.0 # homogeneous linewidth
E0SDStep 50.0 # inhomogeneous linewidth
SDNCStep 1.0 # origin shift along dimensionless normal coordinate
The fit run of orca_asa on the file example008.inp will converge
upon approximately 700 function evaluations (for MWADRelTol=1e-4). The
results of the fit will be stored in file example008.001.inp which has
the same structure as the input file example008.inp. Thus, if the fit
is not satisfactory and/or it is not fully converged it can be refined
in subsequent orca_asa run upon which file example008.002.inp will
be created, and so on. Some model parameters in intermediate files can
be be additionally modified and/or some constraints can be lifted if so
desired. The output file example008.001.inp will contain fitted
displacement parameters \(\left\{{ \Delta_{m} } \right\}\)stored in the
$sdnc block:
$sdnc
7 1
1
1 0.675000
2 -0.194484
3 -0.217527
4 0.811573
5 0.529420
6 -0.149991
7 1.314915
In the present example, these parameters are actually in very close agreement with those published for the hexatriene molecule!
The overall quality of the fit is determined by the parameter MWAD which
upon convergence reaches the value of \(\approx\)0.027.
The fitted rR intensities are presented in the commented lines next to
the experimental rR intensities in file example008.001.inp:
$rrs_exp
1
1 1 3.495285e+001
Ex 39809.00
NT 7
1
Int 10.0 1.0 # simulated intensity: 1.000982e+001
modes 1
quanta 1;
2
Int 5.0 1.0 # simulated intensity: 8.976285e-001
modes 2
quanta 1;
3
Int 1.5 1.0 # simulated intensity: 1.255880e+000
modes 3
quanta 1;
4
Int 21.0 1.0 # simulated intensity: 1.761809e+001
modes 4
quanta 1;
5
Int 7.5 1.0 # simulated intensity: 7.499749e+000
modes 5
quanta 1;
6
Int 2.0 1.0 # simulated intensity: 6.014466e-001
modes 6
quanta 1;
7
Int 46.0 1.0 # simulated intensity: 4.600071e+001
modes 7
quanta 1;
The file hex-abs.fit.dat will contain the experimental and fitted absorption spectra in ASCII format which can be plotted in order to visualize the quality of absorption fit (Fig. 7.56).
Fig. 7.56 Experimental (black) and fitted (red) absorption spectrum corresponding to 1-\(^1\)A\(_g\) \(\rightarrow\) 1-\(^1\)B\(_u\) transition in 1,3,5 trans-hexatriene.¶
NOTE
The more experimental rR intensities are included in the analysis the more reliable is the fit. In principle it is possible to obtain fully consistent results even if only a limited number of vibrational transitions is provided. However, in such a case it is desirable to include into analysis at least a single Raman transition involving the mode for which \(\Delta\) is to be determined.
The quality of the fit can be improved if the IMDHOFA model is invoked and excited-state vibrational frequencies are allowed to vary.
Due to the initial guess and dimension of the simplex, as well as some peculiarities of the simplex algorithm for function minimization, you can still refine the fit by rerunning
orca_asaon fileexample008.001.inpthat may lead to an even lower value of the parameterMWAD = 0.021, and therefore to better agreement of experimental and fitted spectra (even though the previous run has been claimed to be converged).In this respect it appears to be wise to perform the fit in 3 steps:
Fit the preresonance region below the 0-0 vibronic band with a single Lorentzian band, from which the adiabatic transition energy \(E_{0}\), and homogeneous linewidth \(\Gamma\) are obtained. The range for fit of the absorption spectrum can be specified by the
AbsRangekeyword in the%fitblock.Fix \(E_{0}\) and \(\Gamma\), and optimize \(\left\{{ \Delta_{m} } \right\}\) fitting the entire spectral range and rR intensities.
Lift constraints on \(E_{0}\) and \(\Gamma\), and reoptimize simultaneously all parameters.
7.41.3.3. Example: Single-Mode Fit of Absorption and Fluorescence Spectra for 1-\(^1\)A\(_g\) \(\rightarrow\) 1-\(^1\)B\(_{2u}\) Transition in Tetracene¶
In this section we provide an example and discuss the most important aspects of joint fit of fluorescence and absorption spectra. Fig. 7.57 displays the experimental emission and absorption spectra corresponding to 1-\(^1\)A\(_g\) \(\rightarrow\) 1-\(^1\)B\(_{2u}\) transition in tetracene.
Fig. 7.57 Deconvoluted absorption (red) and fluorescence (blue) spectra of tetracene in cyclohexane upon the assumption of a single vibronically active mode. The black solid lines represent experimental spectra.¶
Both spectra show pronounced effective vibrational progressions that are dominated by 3 and 5 peaks, respectively. As can be shown on the basis of quantum chemical calculations this progression has essentially multimode character. However, the experimental spectra can be well fitted under the assumption of a single vibronically active mode. The input has the following structure:
#
# example009.inp
#
# Parameters to be varied:
# 1) adiabatic minima transition energy
# 2) homogeneous and inhomogeneous linewidths
# 3) normal mode frequency and corresponding dimensionless displacement of the
# excited-state origin
#
%sim
Model IMDHO
EnInput E0 # we assume adiabatic minima separation energies
end
%fit
Fit true # global flag to turn on the fit
AbsFit true # flag to include absorption spectrum into the fit
FlFit true # flag to include fluorescence spectrum into the fit
WeightsAdjust true
AbsRange 19000.0, 28000.0 # spectral range for absorption
# which will be included into the fit
FlRange 17800.0, 22300.0 # spectral range for absorption
# which will be considered in the fit
AbsName "absexp.dat" # name of the file containing experimental
# absorption spectrum in a simple two-column
# ASCII format
FlName "flexp.dat" # name of the file with experimental fluorescence spectrum
ExpAbsScaleMode Rel # flags indicating that only relative shapes of the
ExpFlScaleMode Rel # absorption and fluorescence bands will be fitted.
CWAF 1.000 # important parameter to have a balanced relative quality of fit
# of fluorescence and absorption
NMaxFunc 10000 # maximum number of function evaluations in simplex
# algorithm
MWADRelTol= 0.0001 # Relative Tolerance of the Mean Weighted Absolute
# Difference (MWAD) function which specifies the
# convergence criterion
TMStep 0.5 # initial step for the transition dipole moments
# in the simplex fitting
E0SDStep 500.0 # initial step for the inhomogeneous linewidth (Sigma)
FREQGStep 100.00 # initial step for the vibrational frequencies
E0Step 1000.0 # initial step for the transition energies
SSStep 10.0 # initial step for the Stokes shift
GammaStep 100 # initial step for the homogeneous linewidth
SDNCStep 0.5 # initial step for the displacement parameter
end
$el_states
2
1 21100.00 100.00 100.00 1.0000 0.0000 0.0000
2 24000.00 100.00 1000.00 1.0000 0.0000 0.0000
$el_states_c
2
1 1 1 1 0 0 0
2 2 2 2 2 0 0
$abs_bool
2
1 1
2 1
$fl_bool
2
1 1
2 0
$ss
2
1 100.000000
2 0.000000
$ss_c
2
1 1
2 0
$vib_freq_gs
1
1 1500.0
$vib_freq_gs_c
1
1 1
$sdnc
1 2
1 2
1 2.0000000 0.000000
$sdnc_c
1 2
1 2
1 1 0
The parameter CWAF=1.0 in the %fit block specifies the weight of
absorption relative to the weight of fluorescence in the difference
function to be minimized. If this parameter was not specified the
quality of the fit would be biased towards the spectrum with a larger
number of experimental points. In some typical situations where the
error in the measured experimental intensity is expected to be smaller
for absorption than for emission it is desirable to choose the value of
CWAF to be more than 1.0.
In order to account for a broad featureless background signal in the
absorption spectrum above 24000 cm\(^{-1}\), the second band was included
into the analysis and approximated with a Voigt lineshape which means
also that the corresponding frequency in the $vib_freq_gs block and
displacement parameter in the $sdnc block are fixed to zero in the
fit. Thus, the $el_states block contains an initial guess on the
transition energies, transition electric dipole moments and linewidth
parameters for 2 states:
$el_states
2
1 21100.00 100.00 100.00 1.0000 0.0000 0.0000
2 24000.00 100.00 1000.00 1.0000 0.0000 0.0000
The initial value of the adiabatic minima separation energy for the
first state was approximated by the energy corresponding to the first
vibronic peak in the absorption spectrum (21100 cm\(^{-1})\). The
transition energies and linewidth parameters are varied independently as
indicated in the $el_states_c block. Since we allow to fit only
bandshapes, but not the overall intensities of the spectra, only
relative absolute values of the transition electric dipole moments of
two bands are important. Therefore it is reasonable to fix all
components of the transition moment for the first state and vary only
\(M_{x}\) component for the second one:
$el_states_c
2
1 1 1 1 0 0 0
2 2 2 2 2 0 0
Since we assume the absorption by both states and emission only from the first one, it is necessary to include Boolean arrays $abs_bool and $fl_bool which specify states which will be included in the treatment of the absorption and fluorescence spectra, respectively:
$abs_bool
2
1 1 # 1 indicates that the corresponding state will be included in the calculation of
2 1 # absorption
$fl_bool
2
1 1
2 0 # 0 indicates that the corresponding state will be excluded from the calculation
# of emission spectrum
We need also to vary the value of vibrational frequency of the mode
which determines separation of vibrational peaks in the spectra. This is
done via the constraint block $vib_freq_gs_c:
$vib_freq_gs_c
1
1 1
Note that it is meaningless to include into the treatment the Stokes
shift for the second state which give rise to the background signal in
the absorption since the corresponding emission is not present.
Therefore \(\lambda\) for the second state is fixed to zero as indicated
in the $ss block and its constraint counterpart $ss_c:
$ss
2
1 100.000000 # initialization of the Stokes shift for the 1st electronic state
2 0.000000
$ss_c
2
1 1 # the Stokes shift for the 1st electronic state will be varied in the fit
2 0 # the Stokes shift for the 2nd electronic state will be fixed in the fit
The fit run of orca_asa on file example009.inp will converge upon
approximately 700 function evaluations (for MWADRelTol=1e-4). The file
example009.001.inp will contain the fitted effective values of the
vibrational frequency and dimensionless displacement:
\(\omega = 1404 \, \text{cm}^{-1}\), \(\Delta = 1.35\). One can notice that
the fit is rather poor in the low- and high-energy edges of the
absorption and fluorescence spectra, respectively
(Fig. 7.57). The
source of this discrepancy is the single-mode approximation which was
employed here. The quality of the fit can be significantly improved
assuming several modes with non-zero displacement parameters. Note that
in such a case the proper guess on the number of active modes and
corresponding dimensionless displacements can be deduced from quantum
chemical calculations.
7.41.4. Quantum-Chemically Assisted Simulations and Fits of Optical Bandshapes and Resonance Raman Intensities¶
In this section we finally connect the spectra simulation algorithms to actual quantum chemical calculations and outline a detailed approach for the analysis of absorption, fluorescence and resonance Raman spectra within the IMDHO model. Our procedure becomes highly efficient and nearly automatic if analytical excited state derivatives with respect to nuclear displacements are available. However, this availability is not mandatory and hence, spectral predictions may as well be achieved by means of normal mode scan calculations for high-level electronic structure methods for which analytic gradients have not been implemented.
7.41.4.1. Example: Quantum-Chemically Assisted Analysis and Fit of the Absorption and Resonance Raman Spectra for 1-\(^1\)A\(_g\) \(\rightarrow\) 1-\(^1\)B\(_u\) Transition in trans-1,3,5-Hexatriene¶
The following input file for an ORCA run invokes the calculation of the excited-state origin displacements along all normal modes by means of energy and excited state gradient calculations at the ground-state equilibrium geometry. The method is valid for the IMDHO model for which the excited-state energy gradient along a given normal mode and corresponding origin shift are related in a very simple way.
#
# example010.inp
#
# TDDFT BHLYP Normal Mode Gradient Calculation
#
# The keyword NMGrad invokes the normal mode gradient calculation
#
! RKS BHandHLYP TightSCF SV(P) NMGrad
%cis NRoots 1
triplets false
end
%rr
# the nuclear Hessian must have been calculated before - for example by a
# DFT calculation.
HessName= "hexatriene.hess"
states 1 # Perform energy-gradient calculations for the 1st
# excited state.
Tdnc 0.005 # Threshold for dimensionless displacements to be
# included in the input file for spectral simulations
# generated at the end of the program run.
# By default Tdnc= 0.005
ASAInput true # Generate the input file for spectra simulations
end
* xyz 0 1
C -0.003374 0.678229 0.00000
H -0.969173 1.203538 0.00000
C 1.190547 1.505313 0.00000
H 2.151896 0.972469 0.00000
C 1.189404 2.852603 0.00000
H 0.251463 3.423183 0.00000
H 2.122793 3.426578 0.00000
C 0.003374 -0.678229 0.00000
H 0.969172 -1.203538 0.00000
C -1.190547 -1.505313 0.00000
H -2.151897 -0.972469 0.00000
C -1.189404 -2.852603 0.00000
H -0.251463 -3.423183 0.00000
H -2.122793 -3.426578 0.00000
*
In the ORCA run the TDDFT excited state gradient calculations are
performed on top of a TDDFT calculation. Note, that the numbers of the
excited-states which have to be included into analysis and input file
for spectral simulations must be specified after the States keyword in
the %rr block. They should also be consistent with the required number
of roots in the %tddft block. The 1-\(^{1}\)B\(_{u}\) excited state
appears to be the first root in the TDDFT calculation. Therefore,
NRoots=1 in the %tddft block, and States=1 in the %rr block. One
should also provide the name of the file containing the nuclear Hessian
matrix via the HessName keyword in the %rr block. Here we used the
.hess file obtained in a frequency calculation at the BHLYP/SV(P)
level of theory.
After the ORCA calculation you will find in your directory a file called
example010.asa.inp that is appropriate to be used together with the
orca_asa program as defined in the preceding sections.
#
# example010.asa.inp
#
# ASA input
#
%sim
model IMDHO
method Heller
AbsRange 5000.0, 100000.0
NAbsPoints 0
FlRange 5000.0, 100000.0
NFlPoints 0
RRPRange 5000.0, 100000.0
NRRPPoints 0
RRSRange 0.0, 4000.0
NRRSPoints 4000
RRS_FWHM 10.0
AbsScaleMode Ext
FlScaleMode Rel
RamanOrder 0
EnInput E0
CAR 0.800
end
%fit
Fit false
AbsFit false
FlFit false
RRPFit fsalse
RRSFit false
method Simplex
WeightsAdjust true
AbsRange 0.0, 10000000.0
FlRange 0.0, 10000000.0
RRPRange 0.0, 10000000.0
RRSRange 0.0, 10000000.0
AbsName ""
FlName ""
ExpFlScaleMode Rel
ExpAbsScaleMode Rel
CWAR -1.000
CWAF -1.000
NMaxFunc 100
MWADRelTol= 1.000000e-004
SFRRPSimStep= 1.000000e+002
SFRRSSimStep 1.000000e+002
FREQGStep 1.000000e+001
FREQEStep 1.000000e+001
E0Step 3.000000e+002
SSStep 2.000000e+001
TMStep 5.000000e-001
GammaStep 5.000000e+001
E0SDStep 5.000000e+001
SDNCStep 4.000000e-001
end
$el_states
1
1 42671.71 100.00 0.00 1.0725 3.3770 -0.0000
$vib_freq_gs
12
1 359.709864
2 456.925612
3 974.521651
4 1259.779018
5 1356.134238
6 1370.721341
7 1476.878592
8 1724.259894
9 1804.572974
10 3236.588264
11 3244.034359
12 3323.831066
$sdnc
12 1
1
1 -0.594359
2 0.369227
3 -0.132430
4 -0.727616
5 0.406841
6 -0.105324
7 0.177617
8 -0.090105
9 -1.412258
10 0.048788
11 0.021438
12 0.008887
This input file can be used to construct theoretical absorption and rR
spectra. In order to compare experimental and theoretical rR spectra,
it is necessary to use in both cases excitation energies that are
approximately in resonance with the same vibrational transitions in the
absorption spectrum. Therefore, in the case of the absorption spectrum
with resolved or partially resolved vibrational structure it is
necessary to modify the transition energies in the %el_states such
that they coincide with the experimentally observed 0-0 vibrational
peaks. It is also desirable to roughly adjust homogeneous and,
possibly, inhomogeneous linewidth parameters such that the experimental
and calculated absorption spectra show similar slopes in the
preresonance region (below the 0-0 transition). Then the assignment of
experimental rR spectra can be done on the basis of comparison with the
theoretical rR spectra calculated for the corresponding experimental
excitation energies. For the sake of consistency and simplicity it is
better to use those excitation energies which fall into the preresonace
region and/or are in resonance with the 0-0 transition. In the case of
diffuse absorption spectra (i.e. those not showing resolved vibrational
structure) it is also necessary to adjust the theoretical transition
energies and linewidth parameters such that experimental and calculated
positions of absorption maxima roughly coincide, and corresponding
slopes below the maxima have a similar behavior. According to above
mentioned considerations one needs to modify the %el_states block in
the file example010.asa.inp:
$el_states
1
1 39808.0 150.00 0.00 1.0725 3.3770 -0.0000
The calculated absorption spectrum obtained by providing
AbsScaleMode= Rel, AbsRange= 39000, 49000 and NAbsPoints= 2000
is shown in Fig. 7.58. Upon comparison with the experimental spectrum one
can notice that the BHLYP functional gives relatively small
discrepancies with somewhat lower intensity in the low-frequency edge
and larger intensity on the high-energy side of the spectrum. Besides,
there is a noticeable mismatch in the separation between individual
vibronic peaks which is due to overestimation of vibrational frequencies
by the BHLYP functional (typically by \(\approx\) 10%).
You can arbitrarily vary various normal coordinate displacements in
%sdnc block within 10–30% of their values in order to observe
modifications of the calculated spectrum. This will tell you how these
parameters influence the spectrum and probably it will be possible to
obtain better initial guesses for the fit. In the present example you
will find that reduction of the absolute value of the displacement
parameter corresponding to the ninth mode by \(\approx\) 10%, and
reduction of vibrational frequencies by \(\approx\) 10% can noticeably
improve the spectral envelope. Such a quick analysis suggests that
experimentally observed peaks in the absorption spectrum represent
different vibrational transitions corresponding to a single
electronically excited state rather than to different electronic
excitations. This conclusion will be confirmed upon establishing the
fact that the absorption and rR spectra can be successfully fitted based
on the assumption of a single electronic transition.
Fig. 7.58 Experimental and calculated at the BHLYP/SV(P) and B3LYP/SV(P) levels of theory absorption (left panel) and rR spectra (right panel) corresponding to 1-\(^1\)A\(_g\) \(\rightarrow\) 1-\(^1\)B\(_u\) transition in trans-1,3,5-hexatriene.¶
In order to calculate the rR spectrum for experimental excitation
energies you need to specify its value through RRSE keyword in %sim
block as well as possibly to modify the parameters related to the
spectral range and linewidth of rR bands which are suitable for
comparison with the experimental rR spectrum:
# excitation energies (cm**-1) for which rR spectra will be calculated:
RRSE 39808
# full width half maximum of Raman bands in rR spectra (cm**-1):
RRS_FWHM 20
RSRange 0, 4000 # spectral range for simulation of rR spectra (cm**-1)
NRRSPoints 4000 # number of points to simulate rR spectra (cm**-1)
# resonance Raman intensities will be calculated
# for all vibrational states with excitation number
# up to RamanOrder:
RamanOrder 3
The calculated rR spectrum is shown in
Fig. 7.58. In the
input we have invoked the calculation of rR intensities for the
transitions with up to 3 vibrational quanta in the final vibrational
state (RamanOrder = 3). Make sure that the rR intensity pattern in the
given spectral range does not change noticeably upon further increase of
this parameter. Typically, the larger are the normal coordinate
displacements the greater order of Raman scattering is required in the
calculation to account for all the most intense transitions in the rR
spectrum. The inclusion of vibrational transitions beyond the
fundamentals is a particular feature of the orca_asa program.
Comparison of the calculated and experimental rR spectra
(Fig. 7.58) mainly
shows discrepancies in the values of the Raman shifts that are mainly
related to the low accuracy of the vibrational frequencies obtained at
the BHLYP level (typically overestimated by \(\approx\) 10%). However, the
intensity patterns of the calculated and experimental rR spectra show
very nice agreement with experiment that is already sufficient to assign
the experimental peaks to individual vibrational transitions. This can
be done upon examination of file example010.asa.o3.rrs.39808.stk which
provides intensity, Raman shift, and specification for each vibrational
transition. It is actually one of the most consistent procedures that
enables one to identify different fundamental, overtone and combination
bands in the experimentally observed rR spectrum. Such an assignment is
a necessary prerequisite for the fit. The current example is relatively
straightforward since the spectral region 1–1700 cm\(^{-1}\) is actually
dominated by fundamental bands while the most intense overtone and
combination transitions occur at higher frequencies. However, in many
cases even the low-frequency spectral range is characterized by
significant contributions from overtone and combination bands that
sometimes are even more intense than fundamental transitions! Thus,
quantum chemical calculations can greatly facilitate the assignment of
experimental rR bands.
After having performed the assignment it is advisable to discard those
modes from the analysis that are not involved in any of the
experimentally observed fundamental, overtone, or combination rR bands
with noticeable intensities. In the present example these are the modes
6, 8, 10–12 from the input file given above. For these modes it is
implied that the fitted displacement parameters are zero. You will find
that the calculated displacement values are rather small indeed. Also it
is advisable to change the ground-state vibrational frequencies in the
$vib_freq_gs block to their experimental values.
Below is the modified input file for the fit run:
#
# example010-01.asa.inp
#
# ASA input
#
%sim
model IMDHO
method Heller
end
%fit
Fit true
AbsFit true
RRSFit true
AbsExpName "hex-abs.dat"
ExpAbsScaleMode Rel
CWAR 5.0
NMaxFunc 1000
SDNCStep 0.5
end
$el_states
1
1 39808.0 150.00 0.00 -0.8533 -3.3690 -0.0000
$el_states_c
1
1 1 1 0 0 0 0
$vib_freq_gs
7
1 354.0
2 444.0
3 934.0
4 1192.0
5 1290.0
6 1403.0
7 1635.0
$sdnc
7 1
1
1 -0.594359
2 0.369227
3 -0.132430
4 -0.727616
5 0.406841
6 0.177617
7 -1.412258
$sdnc_c
7 1
1
1 1
2 2
3 3
4 4
5 5
6 6
7 7
$rrs_exp
1
1 1
Ex 39809.0
NTr 11
1
int 10.0 1.0
modes 1
quanta 1;
2
int 5.0 1.0
modes 2
quanta 1;
3
int 1.5 1.0
modes 3
quanta 1;
4
int 21.0 1.0
modes 4
quanta 1;
5
int 7.5 1.0
modes 5
quanta 1;
6
int 2.0 1.0
modes 6
quanta 1;
7
int 46.0 1.0
modes 7
quanta 1;
8
int 6.8 1.0
modes 1, 7
quanta 1, 1;
9
int 4.0 1.0
modes 2, 7
quanta 1, 1;
10
int 2.0 1.0
modes 3, 7
quanta 1, 1;
11
int 17.0 1.0
modes 7
quanta 2;
In addition to the experimental intensities of fundamental bands the input file also contains the information about some overtone and combination transitions. Note that it is not really necessary to include all of them them into the fit, in particular if some of the rR bands are strongly overlapping with each other.
Fitted normal coordinate displacements of the excited-state origin show nice agreement with the published values:
$sdnc
7 1
1
1 -0.638244
2 0.455355
3 -0.229126
4 -0.854357
5 0.501219
6 0.197679
7 -1.292997
NOTE
It is not really important to employ the BHLYP/SV(P) method in the frequency calculations in order to obtain the
.hessfile (this was merely done to be consistent with the TDDFT/BHLYP/SV(P) method for the excited-state model parameters calculation). The frequency calculations can for example be carried out at the BP86/TZVP or RI-SCS-MP2/TZVP level of theory. This will provide displacements pattern very similar to that of the BHLYP/SV(P) method, but much more accurate vibrational frequencies which will further facilitate the assignment of rR spectra (Fig. 7.58). However, such a procedure can be inconsistent if the two methods give noticeably different normal mode compositions and/or vibrational frequencies. From our experience it can lead to significant overestimation of the excited-state displacements for some low-frequency modes.It is known that predicted dimensionless normal coordinate displacements critically depend on the fraction of the “exact” Hartree-Fock exchange (EEX) included in hybrid functionals. In general no universal amount of EEX exists that provides a uniformly good description for all systems and states. Typically, for a given molecule either the BHLYP/TZVP (50% of EEX) or B3LYP/TZVP (20% of EEX) methods yields simulated spectra that compare very well with those from experiment if vibrational frequencies are appropriately scaled.
7.41.4.2. Important Notes about Proper Comparison of Experimental and Quantum Chemically Calculated Resonance Raman Spectra¶
In order to compare experimental and theoretical rR spectra, it is
necessary to use in both cases excitation energies that are
approximately in resonance with the same vibrational transitions in the
absorption spectrum. Therefore, in the case of diffuse absorption
spectra (i.e. those not showing resolved vibrational structure) one
needs to adjust the transition energies and linewidth paramters in the
%el_states block such that the envelopes of the experimental and
theoretical spectra rouhgly coincide, and then to employ experimental
values of excitation energies to construct theoretical rR spectra.
Typically in the case of diffuse absorption spectra rR profiles are
rather smooth. Therefore, even though excitation energies are not in
resonance with the same vibrational transition in the absorption
spectrum, the rR spectra are not expected to vary significantly in the
case of such mismatch.
In the case of the absorption spectrum with resolved or partially
resolved vibrational structure it is necessary to modify the transition
energies in the %el_states block such that the calculated and
experimentally observed 0-0 vibrational peaks coincide, and modify
linewidth parameters so that the low-energy slopes in the calculated and
experimental spectra have a similar behavior.
Consider a single-mode model system for which “experimental” and calculated absorption spectra are shown in Fig. 7.59.
Fig. 7.59 Experimental and theoretical absorption spectra for a single-mode model system. The calculated spectrum is adjusted such that the position of 0-0 peak coincide with the experimental one.¶
Comparison of the calculated and experimental spectra shows that some adjustment of the linewidth parameters is neceassy before construction of theoretical rR spectra. One can directly compare calculated and experimental rR spectra upon the excitation at 16200 cm\(^{-1}\) which is in resonance with the 0-0 vibronic band. However, it is not consistent to use experimental values of the excitation energy in the calculation of rR spectrum which is in resonance with one of the other vibronic bands since the separation between vibrational peaks in the experimental and calculated spectra is different whereby positions of the peaks in both spectra do not coincide. Instead one should use the excitaition energy which corresponds to the same vibronic peak in the calculated absorption spectrum as in the experimental one. Alternatively, one can adjust theoretical value of vibrational frequency such that positions of corresponding vibronic peaks in the spectra coincide, and then use experimental values of excitation energies for the calculation of rR spectra.
7.41.4.3. Example: Normal Mode Scan Calculations of Model Parameters for 1-\(^1\)A\(_g\) \(\rightarrow\) 1-\(^1\)B\(_u\) Transition in trans-1,3,5-Hexatriene¶
If excited state gradients are not available (which is the case for many of the electronic structure methods supported by ORCA), you have to resort to a more laborious procedure – single point calculations at geometries that are displaced along the various normal modes of the system. This roughly corresponds to taking numerical derivatives – however, once this extra effort is invested more information can be obtained from the calculation than what would be possible from an analytic derivative calculation.
The present example illustrates the application of normal mode scan calculations for the evaluation of excited state harmonic parameters that are necessary to simulate optical spectra within the IMDHO model. This method can be applied with any method like CIS, CASSCF, MRCI or TD-DFT.
The reference wavefunctions for the multireference calculations reported below are of the state-averaged CASSCF (SA-CASSCF) type. The complete active space CAS(6,6) includes all 6 valence shell \(\pi\)-orbitals. The average is taken over the first four states which was found necessary in order to include the ground state and the strongly allowed 1-\(^{1}\)B\(_{u}\)state.
#
# example011.inp
#
# CASSCF normal mode scan calculations
#
# first do single point RHF calculation
! RHF TZVP TightSCF
* xyz 0 1
C -0.002759 0.680006 0.000000
H -0.966741 1.204366 0.000000
C 1.187413 1.500920 0.000000
H 2.146702 0.969304 0.000000
C 1.187413 2.850514 0.000000
H 0.254386 3.420500 0.000000
H 2.116263 3.422544 0.000000
C 0.002759 -0.680006 0.000000
H 0.966741 -1.204366 0.000000
C -1.187413 -1.500920 0.000000
H -2.146702 -0.969304 0.000000
C -1.187413 -2.850514 0.000000
H -0.254386 -3.420500 0.000000
H -2.116263 -3.422544 0.000000
*
# perform SA-CASSCF calculation upon appropriate rotation of MOs
$new_job
! TZVP TightSCF
%scf
rotate {23,27} end
end
%casscf
nel 6
norb 6
mult 1
nroots 4
end
* xyz 0 1
C -0.002759 0.680006 0.000000
H -0.966741 1.204366 0.000000
C 1.187413 1.500920 0.000000
H 2.146702 0.969304 0.000000
C 1.187413 2.850514 0.000000
H 0.254386 3.420500 0.000000
H 2.116263 3.422544 0.000000
C 0.002759 -0.680006 0.000000
H 0.966741 -1.204366 0.000000
C -1.187413 -1.500920 0.000000
H -2.146702 -0.969304 0.000000
C -1.187413 -2.850514 0.000000
H -0.254386 -3.420500 0.000000
H -2.116263 -3.422544 0.000000
*
# do normal mode scan calculations
# to map CASSCF ground and excited-state PESs
$new_job
! TZVP TightSCF NMScan
%casscf
nel 6
norb 6
mult 1
nroots 4
end
%rr
HessName "hexatriene_bp86.hess"
NMList 10,11,18,24,26,28,29,31,32
NSteps 6
FreqAlter true
EnStep 0.0001
State 3
end
* xyz 0 1
C -0.002759 0.680006 0.000000
H -0.966741 1.204366 0.000000
C 1.187413 1.500920 0.000000
H 2.146702 0.969304 0.000000
C 1.187413 2.850514 0.000000
H 0.254386 3.420500 0.000000
H 2.116263 3.422544 0.000000
C 0.002759 -0.680006 0.000000
H 0.966741 -1.204366 0.000000
C -1.187413 -1.500920 0.000000
H -2.146702 -0.969304 0.000000
C -1.187413 -2.850514 0.000000
H -0.254386 -3.420500 0.000000
H -2.116263 -3.422544 0.000000
*
The file containing the Hessian matrix ("hexatriene_bp86.hess") was
obtained from the BP86/TZVP frequency calculations. The keyword NMList
provides the list of the normal modes to be scanned. These should be
only the totally symmetric vibrations, since only they can be
significant for absorption and resonance Raman spectra within the
constraints of the IMDHO model. The FreqAlter flag indicates whether
frequency alterations are assumed in the post-scan potential surface
fit. The Parameter EnStep is used to select the appropriate step
during the scan calculations. The value is chosen such that the average
energy change (in Eh) in both directions is not less than this
parameter.