12.2 Chemical Solvent Models

12.2.3 PCM Job Control

A PCM calculation is requested by setting SOLVENT_METHOD = PCM in the $rem section. As mentioned above, there are a variety of different theoretical models that fall within the PCM family, so additional fine-tuning may be required, as described below.

12.2.3.1 $pcm section

Most PCM job control is accomplished via options specified in the $pcm input section, which allows the user to specify which flavor of PCM will be used, which algorithm will be used to solve the PCM equations, and other options. The format of the $pcm section is analogous to that of the $rem section:

$pcm
   <Keyword>  <parameter/option>
$end

Note:  The following job control variables belong only in the $pcm section. Do not place them in the $rem section.

Theory
       Specifies the which polarizable continuum model will be used.
INPUT SECTION: $pcm
TYPE:
       STRING
DEFAULT:
       CPCM
OPTIONS:
       CPCM Conductor-like PCM with fε=(ε-1)/ε. COSMO Original conductor-like screening model with fε=(ε-1)/(ε+1/2). IEFPCM IEF-PCM with an asymmetric 𝐊 matrix. SSVPE SS(V)PE model, equivalent to IEF-PCM with a symmetric 𝐊 matrix.
RECOMMENDATION:
       The IEF-PCM/SS(V)PE model is more sophisticated model than either C-PCM or COSMO, and probably more appropriate for low-dielectric solvents, but it is also more computationally demanding. In high-dielectric solvents there is little difference between these models. Note that the keyword COSMO in this context simply affects the dielectric screening factor fε; to obtain the outlying charge correction suggested by Klamt,472, 50 one should use SOLVENT_METHOD = COSMO rather than SOLVENT_METHOD = PCM. (See Section 12.2.7.)

Method
       Specifies which surface discretization method will be used.
INPUT SECTION: $pcm
TYPE:
       STRING
DEFAULT:
       SWIG
OPTIONS:
       SWIG Switching/Gaussian method ISWIG “Improved” Switching/Gaussian method with an alternative switching function Spherical Use a single, fixed sphere for the cavity surface. Fixed Use discretization point charges instead of smooth Gaussians.
RECOMMENDATION:
       Use of SWIG is recommended only because it is slightly more efficient than the switching function of ISWIG. On the other hand, ISWIG offers some conceptually more appealing features and may be superior in certain cases. Consult Refs. 520, 521 for a discussion of these differences. The Fixed option uses the Variable Tesserae Number (VTN) algorithm of Li and Jensen,563 with Lebedev grid points. VTN uses point charges with no switching function or Gaussian blurring, and is therefore subject to discontinuities in geometry optimizations. It is not recommended, except to make contact with other calculations in the literature.

SwitchThresh
       Threshold for discarding grid points on the cavity surface.
INPUT SECTION: $pcm
TYPE:
       INTEGER
DEFAULT:
       8
OPTIONS:
       n Discard grid points when the switching function is less than 10-n.
RECOMMENDATION:
       Use the default, which is found to avoid discontinuities within machine precision. Increasing n reduces the cost of PCM calculations but can introduce discontinuities in the potential energy surface.

Construction of the solute cavity is an important part of the model and users should consult the literature in this capacity, especially with regard to the radii used for the atomic spheres. The default values provided in Q-Chem correspond to the consensus choice that has emerged over several decades, namely, to use vdW radii scaled by a factor of 1.2. The most widely-used set of vdW radii are those determined from crystallographic data by Bondi,106 although the radius for hydrogen was later adjusted to 1.1 Å,795 and radii for those main-group elements not addressed by Bondi were provided later.600 This extended set of vdW is used by default in Q-Chem, and for simplicity we call these “Bondi radii” regardless of whether they come from Bondi’s original paper or the later work. Alternatively, atomic radii from the Universal Force Field (UFF) are available.766 The main appeal of UFF radii is that they are defined for all atoms of the periodic table, though the quality of these radii for PCM applications is unclear. Finally, the user may specify his or her own radii for cavity construction using a $van_der_waals input section, the format for which is described in Section 12.2.9. No scaling factor is applied to user-defined radii. Note that R=0 is allowed for a particular atomic radius, in which case the atom in question is not used to construct the cavity surface. This feature facilitates the construction of “united atom” cavities,55 in which the hydrogen atoms do not get their own spheres and the heavy-atom radii are increased to compensate Finally, since the solvent molecules should not be able to penetrate all the way to the atomic vdW radii of the solute, it is traditional either to scale the atomic radii (vdW surface construction) or else to augment them with an assumed radius of a spherical solvent molecule (SAS construction), but not both.

Radii
       Specifies which set of atomic van der Waals radii will be used to define the solute cavity.
INPUT SECTION: $pcm
TYPE:
       STRING
DEFAULT:
       BONDI
OPTIONS:
       BONDI Use the (extended) set of Bondi radii. FF Use Lennard-Jones radii from a molecular mechanics force field. UFF Use radii form the Universal Force Field. READ Read the atomic radii from a $van_der_waals input section.
RECOMMENDATION:
       Bondi radii are widely used. The FF option requires the user to specify an MM force field using the FORCE_FIELD $rem variable, and also to define the atom types in the $molecule section (see Section 12.3). This is not required for UFF radii.

vdwScale
       Scaling factor for the atomic van der Waals radii used to define the solute cavity.
INPUT SECTION: $pcm
TYPE:
       FLOAT
DEFAULT:
       1.2
OPTIONS:
       f Use a scaling factor of f>0.
RECOMMENDATION:
       The default value is widely used in PCM calculations, although a value of 1.0 might be appropriate if using a solvent-accessible surface.

SASradius
       Form a “solvent accessible” surface with the given solvent probe radius.
INPUT SECTION: $pcm
TYPE:
       FLOAT
DEFAULT:
       0.0
OPTIONS:
       r Use a solvent probe radius of r, in Å.
RECOMMENDATION:
       The solvent probe radius is added to the scaled van der Waals radii of the solute atoms. A common solvent probe radius for water is 1.4 Å, but the user should consult the literature regarding the use of solvent-accessible surfaces.

SurfaceType
       Selects the solute cavity surface construction.
INPUT SECTION: $pcm
TYPE:
       STRING
DEFAULT:
       VDW_SAS
OPTIONS:
       VDW_SAS van der Waals or solvent-accessible surface SES solvent-excluded surface
RECOMMENDATION:
       The vdW surface and the SAS are each comprised simply of atomic spheres and thus share a common option; the only difference is the specification of a solvent probe radius, SASradius. For a true vdW surface, the probe radius should be zero (which is the default), whereas for the SAS the atomic radii are traditionally not scaled, hence vdwScale should be set to zero (which is not the default). For the SES, only SWIG discretization is available, but this can be used with any set of (scaled or unscaled) atomic radii, or with radii that are augmented by SASradius.

Historically, discretization of the cavity surface has involved “tessellation” methods that divide the cavity surface area into finite polygonal “tesserae”. (The GEPOL algorithm698 is perhaps the most widely-used tessellation scheme.) Tessellation methods, however, suffer not only from discontinuities in the cavity surface area and solvation energy as a function of the nuclear coordinates, but in addition they lead to analytic energy gradients that are complicated to derive and implement. To avoid these problems, Q-Chem’s SWIG PCM implementation519, 520, 521 uses Lebedev grids to discretize the atomic spheres. These are atom-centered grids with icosahedral symmetry, and may consist of anywhere from 26 to 5294 grid points per atomic sphere. The default values used by Q-Chem were selected based on extensive numerical tests,520, 521 and they are looser for MM atoms (in MM/PCM or QM/MM/PCM jobs) than they are for QM atoms, reflecting the more complicated electrostatic potential that is generated by a QM density as compared to an MM point charge. For QM atoms, the default is to use N=110 points for hydrogen atoms and N=194 points for all other atoms, whereas for MM atoms the default is N=50 for hydrogen and N=110 for non-hydrogen. These default values exhibit good rotational invariance (<0.1 kcal/mol differences in ΔG when the molecule is rotated520) and absolute solvation energies that typically lie within <1 kcal/mol of the N limit,520, 521 at least for charge-neutral solutes.

Note that earlier versions of Q-Chem used denser grids by default. (In versions up to and including Q-Chem v. 4.2, the default was N=590 for all QM atoms, but was switched to N=302 beginning with v. 4.2.1. The defaults mentioned above are the current ones starting with v. 5.2.) However, grid errors of 0.5 kcal/mol are well within the intrinsic accuracy of ΔGsolvation for these models. Grid errors in solvatochromatic shifts for excitation energies tend to be 0.01–0.02 eV, which is well within the intrinsic accuracy of nearly any excited-state methodology. If questions about grid accuracy arise, we suggest using N=302 as a high-quality option and N=590 as an essentially converged option.520, 521

Note:  The acceptable values for the number of Lebedev points per sphere are N=26, 50, 110, 194, 302, 434, 590, 770, 974, 1202, 1454, 1730, 2030, 2354, 2702, 3074, 3470, 3890, 4334, 4802, or 5294.

HeavyPoints
       The number of Lebedev grid points to be placed non-hydrogen atoms in the QM system.
INPUT SECTION: $pcm
TYPE:
       INTEGER
DEFAULT:
       194
OPTIONS:
       Acceptable values are listed above.
RECOMMENDATION:
       Use the default for geometry optimizations. For absolute solvation energies, the user may want to examine convergence with respect to N.

HPoints
       The number of Lebedev grid points to be placed on H atoms in the QM system.
INPUT SECTION: $pcm
TYPE:
       INTEGER
DEFAULT:
       110
OPTIONS:
       Acceptable values are listed above.
RECOMMENDATION:
       Use the default for geometry optimizations. For absolute solvation energies, the user may want to examine convergence with respect to N.

MMHeavyPoints
       The number of Lebedev grid points to be placed on non-hydrogen atoms in the MM subsystem.
INPUT SECTION: $pcm
TYPE:
       INTEGER
DEFAULT:
       110
OPTIONS:
       Acceptable values are listed above.
RECOMMENDATION:
       Use the default for geometry optimizations. For absolute solvation energies, the user may want to examine convergence with respect to N. This option applies only to MM/PCM or QM/MM/PCM calculations.

MMHPoints
       The number of Lebedev grid points to be placed on H atoms in the MM subsystem.
INPUT SECTION: $pcm
TYPE:
       INTEGER
DEFAULT:
       50
OPTIONS:
       Acceptable values are listed above.
RECOMMENDATION:
       Use the default for geometry optimizations. For absolute solvation energies, the user may want to examine convergence with respect to N. This option applies only to MM/PCM or QM/MM/PCM calculations.

Especially for complicated molecules, the user may want to visualize the cavity surface. This can be accomplished by setting PrintLevel 2, which will trigger the generation of several .PQR files that describe the cavity surface. (These are written to the Q-Chem output file.) The .PQR format is similar to the common .PDB (Protein Data Bank) format, but also contains charge and radius information for each atom. One of the output .PQR files contains the charges computed in the PCM calculation and radii (in Å) that are half of the square root of the surface area represented by each surface grid point. Thus, in examining this representation of the surface, larger discretization points are associated with larger surface areas. A second .PQR file contains the solute’s electrostatic potential (in atomic units), in place of the charge information, and uses uniform radii for the grid points. These .PQR files can be visualized using various third-party software, including the freely-available Visual Molecular Dynamics (VMD) program,W. Humphrey, A. Dalke, and K. Schulten (1996), 17 which is particularly useful for coloring the .PQR surface grid points according to their charge, and sizing them according to their contribution to the molecular surface area. (Examples of such visualizations can be found in Ref. 519.)

PrintLevel
       Controls the printing level during PCM calculations.
INPUT SECTION: $pcm
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 Prints PCM energy and basic surface grid information. Minimal additional printing. 1 Level 0 plus PCM solute-solvent interaction energy components and Gauss’ Law error. 2 Level 1 plus surface grid switching parameters and a .PQR file for visualization of the cavity surface apparent surface charges. 3 Level 2 plus a .PQR file for visualization of the electrostatic potential at the surface grid created by the converged solute. 4 Level 3 plus additional surface grid information, electrostatic potential and apparent surface charges on each SCF cycle. 5 Level 4 plus extensive debugging information.
RECOMMENDATION:
       Use the default unless further information is desired.

Finally, note that setting Method to Spherical in the $pcm input selection requests the construction of a solute cavity consisting of a single, fixed sphere. This is generally not recommended but is occasionally useful for making contact with the results of Born models in the literature, or the Kirkwood-Onsager model discussed in Section 12.2.1. In this case, the cavity radius and its center must also be specified in the $pcm section. The keyword HeavyPoints controls the number of Lebedev grid points used to discretize the surface.

CavityRadius
       Specifies the solute cavity radius.
INPUT SECTION: $pcm
TYPE:
       FLOAT
DEFAULT:
       None
OPTIONS:
       R Use a radius of R, in Ångstroms.
RECOMMENDATION:
       None.

CavityCenter
       Specifies the center of the spherical solute cavity.
INPUT SECTION: $pcm
TYPE:
       FLOAT
DEFAULT:
       0.0 0.0 0.0
OPTIONS:
       x y z Coordinates of the cavity center, in Ångstroms.
RECOMMENDATION:
       The format is CavityCenter followed by three floating-point values, delineated by spaces. Uses the same coordinate system as the $molecule section.

12.2.3.2 Examples

The following example shows a very basic PCM job. The solvent dielectric is specified in the $solvent section, which is described below.

Example 12.3  A basic example of using the PCMs: optimization of trifluoroethanol in water.

$molecule
   0 1
   C    -0.245826    -0.351674    -0.019873
   C     0.244003     0.376569     1.241371
   O     0.862012    -0.527016     2.143243
   F     0.776783    -0.909300    -0.666009
   F    -0.858739     0.511576    -0.827287
   F    -1.108290    -1.303001     0.339419
   H    -0.587975     0.878499     1.736246
   H     0.963047     1.147195     0.961639
   H     0.191283    -1.098089     2.489052
$end

$rem
   JOBTYPE         OPT
   BASIS           6-31G*
   METHOD          B3LYP
   SOLVENT_METHOD  PCM
$end

$pcm
   Theory          CPCM
   Method          SWIG
   Solver          Inversion
   HeavyPoints     194
   HPoints         194
   Radii           Bondi
   vdwScale        1.2
$end

$solvent
   Dielectric 78.39
$end

The next example uses a single spherical cavity and should be compared to the Kirkwood-Onsager job, Example 12.12.2.1 on page 12.2.1.

Example 12.4  PCM with a single spherical cavity, applied to H2O in acetonitrile

$molecule
   0 1
   O       0.00000000     0.00000000     0.11722303
   H      -0.75908339     0.00000000    -0.46889211
   H       0.75908339     0.00000000    -0.46889211
$end

$rem
   METHOD            HF
   BASIS             6-31g**
   SOLVENT_METHOD    pcm
$end

$pcm
   method        spherical   ! single spherical cavity with 590 discretization points
   HeavyPoints   590
   CavityRadius  1.8         ! Solute Radius, in Angstrom
   CavityCenter  0.0 0.0 0.0 ! Will be at center of Standard Nuclear Orientation
   Theory        SSVPE
$end

$solvent
   Dielectric        35.9   !   Acetonitrile
$end

Finally, we consider an example of a united-atom cavity. Note that a user-defined van der Waals radius is supplied only for carbon, so the hydrogen radius is taken to be zero and thus the hydrogen atoms are not used to construct the cavity surface. (As mentioned above, the format for the $van_der_waals input section is discussion in Section 12.2.9).

Example 12.5  United-atom cavity construction for ethylene.

$comment
   Benzene (in benzene), with a united-atom cavity construction
   R = 2.28 A for carbon, R = 0 for hydrogen
$end

$molecule
   0 1
   C    1.38620    0.000000   0.000000
   C    0.69310    1.200484   0.000000
   C   -0.69310    1.200484   0.000000
   C   -1.38620    0.000000   0.000000
   C   -0.69310   -1.200484   0.000000
   C    0.69310   -1.200484   0.000000
   H    2.46180    0.000000   0.000000
   H    1.23090    2.131981   0.000000
   H   -1.23090    2.131981   0.000000
   H   -2.46180    0.000000   0.000000
   H   -1.23090   -2.131981   0.000000
   H    1.23090   -2.131981   0.000000
$end

$rem
   EXCHANGE        hf
   BASIS           6-31G*
   SOLVENT_METHOD  pcm
$end

$pcm
   theory          iefpcm   ! this is a synonym for ssvpe
   method          swig
   printlevel      1
   radii           read
$end

$solvent
   dielectric 2.27
$end

$van_der_waals
1
  6     2.28
  1     0.00
$end

12.2.3.3 $solvent section

The solvent for PCM calculations is specified using the $solvent section, as documented below. In addition, the $solvent section can be used to incorporate non-electrostatic interaction terms into the solvation energy. (The Theory keyword in the $pcm section specifies only how the electrostatic interactions are handled.) The general form of the $solvent input section is shown below. The $solvent section was used above to specify parameters for the Kirkwood-Onsager SCRF model, and will be used again below to specify the solvent for SMx calculations (Section 12.2.8); in each case, the particular options that can be listed in the $solvent section depend upon the value of the $rem variable SOLVENT_METHOD.

$solvent
   NonEls  <Option>
   NSolventAtoms <Number unique of solvent atoms>
   SolventAtom <Number1> <Number2> <Number3> <SASradius>
   SolventAtom <Number1> <Number2> <Number3> <SASradius>
   . . .
   <Keyword>  <parameter/option>
   . . .
$end

The keyword SolventAtom requires multiple parameters, whereas all other keywords require only a single parameter. In addition to any (optional) non-electrostatic parameters, the $solvent section is also used to specify the solvent’s dielectric constant. If non-electrostatic interactions are ignored, then this is the only keyword that is necessary in the $solvent section. For nonequilibrium TDDFT/C-PCM calculations (Section 12.2.2.3), the optical dielectric constant should be specified in the $solvent section as well.

Dielectric
       The (static) dielectric constant of the PCM solvent.
INPUT SECTION: $solvent
TYPE:
       FLOAT
DEFAULT:
       78.39
OPTIONS:
       ε Use a dielectric constant of ε>0.
RECOMMENDATION:
       The static (i.e., zero-frequency) dielectric constant is what is usually called “the” dielectric constant. The default corresponds to water at 25C.

OpticalDielectric
       The optical dielectric constant of the PCM solvent.
INPUT SECTION: $solvent
TYPE:
       FLOAT
DEFAULT:
       1.78
OPTIONS:
       ε Use an optical dielectric constant of ε>0.
RECOMMENDATION:
       The default corresponds to water at 25C. Note that ε=n2, where n is the solvent’s index of refraction.

The non-electrostatic interactions currently available in Q-Chem are based on the work of Cossi et al.,193 and are computed outside of the SCF procedure used to determine the electrostatic interactions. The non-electrostatic energy is highly dependent on the input parameters and can be extremely sensitive to the radii chosen to define the solute cavity. Accordingly, the inclusion of non-electrostatic interactions is highly empirical and probably needs to be considered on a case-by-case basis. Following Ref. 193, the cavitation energy is computed using the same solute cavity that is used to compute the electrostatic energy, whereas the dispersion/repulsion energy is computed using a solvent-accessible surface.

The following keywords (in the $solvent section) are used to define non-electrostatic parameters for PCM calculations.

NonEls
       Specifies what type of non-electrostatic contributions to include.
INPUT SECTION: $solvent
TYPE:
       STRING
DEFAULT:
       None
OPTIONS:
       Cav Cavitation energy Buck Buckingham dispersion and repulsion energy from atomic number LJ Lennard-Jones dispersion and repulsion energy from force field BuckCav Buck + Cav LJCav LJ + Cav
RECOMMENDATION:
       A very limited set of parameters for the Buckingham potential is available at present.

NSolventAtoms
       The number of different types of atoms.
INPUT SECTION: $solvent
TYPE:
       INTEGER
DEFAULT:
       None
OPTIONS:
       N Specifies that there are N different types of atoms.
RECOMMENDATION:
       This keyword is necessary when NonEls = Buck, LJ, BuckCav, or LJCav. Methanol (CH3OH), for example, has three types of atoms (C, H, and O).

SolventAtom
       Specifies a unique solvent atom.
INPUT SECTION: $solvent
TYPE:
       Various
DEFAULT:
       None.
OPTIONS:
       Input (TYPE) Description Number1 (INTEGER): The atomic number of the atom Number2 (INTEGER): How many of this atom are in a solvent molecule Number3 (INTEGER): Force field atom type SASradius (FLOAT): Probe radius (in Å) for defining the solvent accessible surface
RECOMMENDATION:
       If not using LJ or LJCav, Number3 should be set to 0. The SolventAtom keyword is necessary when NonEls = Buck, LJ, BuckCav, or LJCav.

Temperature
       Specifies the solvent temperature.
INPUT SECTION: $solvent
TYPE:
       FLOAT
DEFAULT:
       300.0
OPTIONS:
       T Use a temperature of T, in Kelvin.
RECOMMENDATION:
       Used only for the cavitation energy.

Pressure
       Specifies the solvent pressure.
INPUT SECTION: $solvent
TYPE:
       FLOAT
DEFAULT:
       1.0
OPTIONS:
       P Use a pressure of P, in bar.
RECOMMENDATION:
       Used only for the cavitation energy.

SolventRho
       Specifies the solvent number density
INPUT SECTION: $solvent
TYPE:
       FLOAT
DEFAULT:
       Determined for water, based on temperature.
OPTIONS:
       ρ Use a density of ρ, in molecules/Å3.
RECOMMENDATION:
       Used only for the cavitation energy.

SolventRadius
       The radius of a solvent molecule of the PCM solvent.
INPUT SECTION: $solvent
TYPE:
       FLOAT
DEFAULT:
       None
OPTIONS:
       r Use a radius of r, in Å.
RECOMMENDATION:
       Used only for the cavitation energy.

The following example illustrates the use of the non-electrostatic interactions.

Example 12.6  Optimization of trifluoroethanol in water using both electrostatic and non-electrostatic PCM interactions. OPLSAA parameters are used in the Lennard-Jones potential for dispersion and repulsion.

$molecule
   0 1
   C    -0.245826    -0.351674    -0.019873     23
   C     0.244003     0.376569     1.241371     22
   O     0.862012    -0.527016     2.143243     24
   F     0.776783    -0.909300    -0.666009     26
   F    -0.858739     0.511576    -0.827287     26
   F    -1.108290    -1.303001     0.339419     26
   H    -0.587975     0.878499     1.736246     27
   H     0.963047     1.147195     0.961639     27
   H     0.191283    -1.098089     2.489052     25
$end

$rem
   JOBTYPE        OPT
   BASIS          6-31G*
   METHOD         B3LYP
   SOLVENT_METHOD PCM
   FORCE_FIELD    OPLSAA
$end

$pcm
   Theory      CPCM
   Method      SWIG
   Solver      Inversion
   HeavyPoints 194
   HPoints     194
   Radii       Bondi
   vdwScale    1.2
$end

$solvent
   NonEls        LJCav
   NSolventAtoms 2
   SolventAtom   8 1 186 1.30
   SolventAtom   1 2 187 0.01
   SolventRadius 1.35
   Temperature   298.15
   Pressure      1.0
   SolventRho    0.03333
   Dielectric    78.39
$end

12.2.3.4 Job control and Examples for Non-Equilibrium Solvation

The OpticalDielectric keyword in $solvent is always needed. The LR energy is automatically calculated while the CIS/TDDFT calculations are performed with PCM, but it is turned off while the perturbation scheme is employed.

ChargeSeparation
       Partition fast and slow charges in solvent equilibrium state
INPUT SECTION: $pcm
TYPE:
       STRING
DEFAULT:
       No default.
OPTIONS:
       Marcus Do slow-fast charge separation in the ground state. Excited Do slow-fast charge separation in an excited-state.
RECOMMENDATION:
       Charge separation is used in conjunction with the StateSpecific keyword in $pcm.

StateSpecific
       Specifies which the state-specific method will be used.
INPUT SECTION: $pcm
TYPE:
       Various
DEFAULT:
       No default.
OPTIONS:
       Marcus Run self-consistent SS method in the ground-state with a given slow polarization charges. Perturb Perform ptSS and ptLR for vertical excitations. i The ith excited-state used for charge separation (for emission).
RECOMMENDATION:
      

NoneqGrad
       Control whether perform excited state geometry optimization in equilibrium or nonequilibrium.
INPUT SECTION: $pcm
TYPE:
       NONE
DEFAULT:
       No default.
OPTIONS:
      
RECOMMENDATION:
       Specify it for nonequilibrium optimization otherwise equilibrium geometry optimization will be performed.

Example 12.7  LR-TDDFT/C-PCM low-lying vertical excitation energy

$molecule
   0 1
   C    0  0  0.0
   O    0  0  1.21
$end

$rem
   EXCHANGE            B3LYP
   CIS_N_ROOTS         10
   CIS_SINGLETS        TRUE
   CIS_TRIPLETS        TRUE
   RPA                 TRUE
   BASIS               6-31+G*
   SOLVENT_METHOD      PCM
$end

$pcm
   Theory      CPCM
   Method      SWIG
   Solver      Inversion
   Radii       Bondi
$end

$solvent
   Dielectric         78.39
   OpticalDielectric  1.777849
$end

Example 12.8  PCM solvation effects on the vertical excitation energies of planar DMABN using the ptSS and ptLR methods.

$molecule
   0  1
   C     0.000046   -0.000398    1.904953
   C     1.210027    0.000379    1.186051
   C     1.214640   -0.000065   -0.194515
   C     0.000164   -0.000616   -0.933832
   C    -1.214349   -0.001557   -0.194687
   C    -1.209753   -0.001846    1.185775
   H     2.151949    0.001377    1.722018
   H     2.164371    0.000481   -0.709640
   H    -2.164082   -0.002008   -0.709781
   H    -2.151763   -0.002287    1.721615
   C    -0.000227    0.001061    3.325302
   N    -0.000475    0.002405    4.484321
   N     0.000053   -0.000156   -2.297372
   C    -1.258656    0.001284   -3.036994
   H    -1.041042    0.001615   -4.102376
   H    -1.860897   -0.885647   -2.811117
   H    -1.859247    0.889133   -2.810237
   C     1.258563   -0.000660   -3.037285
   H     1.860651    0.886208   -2.810755
   H     1.859362   -0.888604   -2.811461
   H     1.040664   -0.000097   -4.102609
$end

$rem
   EXCHANGE              LRC-wPBEPBE
   OMEGA                 260
   BASIS                 6-31G*
   CIS_N_ROOTS           10
   RPA                   2
   CIS_SINGLETS          1
   CIS_TRIPLETS          0
   CIS_DYNAMIC_MEM       TRUE
   CIS_RELAXED_DENSITY   TRUE
   USE_NEW_FUNCTIONAL    TRUE
   SOLVENT_METHOD        PCM
   PCM_PRINT             1
$end

$pcm
   NonEquilibrium
   Theory                 IEFPCM
   StateSpecific          Perturb
$end

$solvent
   Dielectric             35.688000       ! Acetonitrile
   OpticalDielectric      1.806874
$end

Example 12.9  Aqueous phenol ionization using state-specific nonequilibrium PCM

$molecule
   0  1
   C  -0.189057  -1.215927  -0.000922
   H  -0.709319  -2.157526  -0.001587
   C   1.194584  -1.155381  -0.000067
   H   1.762373  -2.070036  -0.000230
   C   1.848872   0.069673   0.000936
   H   2.923593   0.111621   0.001593
   C   1.103041   1.238842   0.001235
   H   1.595604   2.196052   0.002078
   C  -0.283047   1.185547   0.000344
   H  -0.862269   2.095160   0.000376
   C  -0.929565  -0.042566  -0.000765
   O  -2.287040  -0.159171  -0.001759
   H  -2.663814   0.725029   0.001075
$end

$rem
  EXCHANGE              wPBE
  CORRELATION           PBE
  LRC_DFT               1
  OMEGA                 300
  BASIS                 6-31+G*
  SCF_CONVERGENCE       8
  SOLVENT_METHOD        PCM
  PCM_PRINT             1
$end

$pcm
   NonEquilibrium
$end

$solvent
   Dielectric            78.39
   OpticalDielectric     1.777849
$end

@@@

$molecule
 1  2
 read
$end

$rem
   EXCHANGE              wPBE
   CORRELATION           PBE
   LRC_DFT               1
   OMEGA                 300
   BASIS                 6-31+G*
   SCF_CONVERGENCE       8
   SOLVENT_METHOD        PCM
   PCM_PRINT             1
   SCF_GUESS             READ
$end

$pcm
   StateSpecific         Marcus
$end

$solvent
   Dielectric            78.39
   OpticalDielectric     1.777849
$end

Example 12.10  PCM solvation effects on the emission energy of twisted DMABN in acetonitrile.

$molecule
   0  1
   C    -0.000002   -0.000003    1.894447
   C     1.230178    0.000003    1.160765
   C     1.244862    0.000001   -0.200360
   C     0.000003   -0.000013   -0.917901
   C    -1.244845   -0.000000   -0.200354
   C    -1.230160    0.000000    1.160753
   H     2.171128    0.000013    1.704064
   H     2.180670    0.000009   -0.750140
   H    -2.180657    0.000006   -0.750120
   H    -2.171112    0.000006    1.704037
   C    -0.000023   -0.000002    3.293509
   N    -0.000011   -0.000001    4.459415
   N    -0.000008   -0.000005   -2.309193
   C     0.000001    1.253881   -3.021235
   H     0.000005    1.099076   -4.098660
   H    -0.882908    1.818975   -2.705815
   H     0.882911    1.818967   -2.705805
   C    -0.000009   -1.253886   -3.021246
   H     0.882917   -1.818966   -2.705849
   H    -0.882901   -1.818992   -2.705803
   H    -0.000038   -1.099071   -4.098670
$end

$rem
   EXCHANGE              LRC-wPBEPBE
   OMEGA                 280
   BASIS                 6-31G*
   CIS_N_ROOTS           10
   RPA                   2
   CIS_SINGLETS          1
   CIS_TRIPLETS          0
   CIS_DYNAMIC_MEM       TRUE
   CIS_RELAXED_DENSITY   TRUE
   USE_NEW_FUNCTIONAL    TRUE
   SOLVENT_METHOD        PCM
   PCM_PRINT             1
$end

$pcm
   ChargeSeparation       Excited
   StateSpecific          1
$end

$solvent
   Dielectric             35.688000   ! Acetonitrile
   OpticalDielectric      1.806874
$end

@@@
$molecule
   READ
$end

$rem
   EXCHANGE              LRC-wPBEPBE
   OMEGA                 280
   BASIS                 6-31G*
   SCF_GUESS             READ
   SCF_CONVERGENCE       8
   SOLVENT_METHOD        PCM
   PCM_PRINT             1
$end

$pcm
   StateSpecific          Marcus
$end

$solvent
   Dielectric             35.688000   ! Acetonitrile
   OpticalDielectric      1.806874
$end