6.9. Solvation

ORCA features several implicit solvation models, including the fully integrated “conductor-like polarizable continuum (C-PCM)” and “Minnesota SMD” solvation models, which are available in all its components. With these models, various types of calculations can be performed using a polarizable continuum with a realistic van der Waals cavity as summarized below:

  • Energies of molecules in solution with a finite dielectric constant \(\varepsilon\) using HF or any DFT method.

  • Optimization of molecular structures in solution using HF or any DFT method with analytic gradients.

  • Calculation of vibrational frequencies using the analytic Hessian for HF or any DFT method, provided that the same calculation is available in vacuum.

  • Calculation of solvent effects on response properties like polarizabilities through coupled-perturbed SCF theory. For magnetic response properties, such as the g-tensor, the C-PCM response vanishes.

  • Calculations of solvent shifts on transition energies using the time-dependent DFT or CIS method. The refractive index of the solvent needs to be provided in addition to the dielectric constant.

  • First order perturbation estimate of solvent effects on state and transition energies in multireference perturbation and configuration-interaction calculations.

Other implicit solvation strategies are available in ORCA. In particular, an interface to the open source implementation of the COSMO-RS model (openCOSMO-RS), as well as different solvation models that can be used in XTB (ALPB, ddCOSMO, and CPCM-X). A detailed overview of the available implicit solvation methods and their usage is provided in Sections ONIOM Methods, and Implicit Solvation Models.

As a simple example, let us compute the solvent effect on the \(n\to \pi^{\ast }\) transition energy in formaldehyde with the C-PCM model. This effect can be obtained by subtracting the solution-phase and gas-phase transition energies. The gas-phase transition energy (4.633 eV) can be computed by using the following input:

! def2-TZVP

%cis nroots 1 end

*int 0 1
 C     0   0   0   0.000000     0.000     0.000
 O     1   0   0   1.200371     0.000     0.000
 H     1   2   0   1.107372   121.941     0.000
 H     1   2   3   1.107372   121.941   180.000
*

By adding the CPCM(water) flag to the input used for the gas-phase calculation, the transition energy can now be computed using the C-PCM model with water as the solvent:

! def2-TZVP CPCM(water)

%cis nroots 1 end

*int 0 1
 C     0   0   0   0.000000     0.000     0.000
 O     1   0   0   1.200371     0.000     0.000
 H     1   2   0   1.107372   121.941     0.000
 H     1   2   3   1.107372   121.941   180.000
*

This C-PCM calculation yields a transition energy of 4.857 eV:

-----------------------------
CIS-EXCITED STATES (SINGLETS)
-----------------------------

the weights of the individual excitations are printed if larger than 1.0e-02

STATE  1:  E=   0.178499 au      4.857 eV    39176.0 cm**-1 <S**2> =   0.000000
7a ->   8a  :     0.929287 (c= -0.96399514)
7a ->  13a  :     0.039268 (c=  0.19816055)
7a ->  18a  :     0.016344 (c=  0.12784298)

Hence, water environment increases the transition energy by 0.224 eV. This increase can be attributed to the stabilization of lone pair orbitals by the presence of water molecules.