Ab initio quantum chemistry makes possible the study of gasphase molecular properties from first principles. In liquid solution, however, these properties may change significantly, especially in polar solvents. Although it is possible to model solvation effects by including explicit solvent molecules in the quantumchemical calculation (e.g. a supermolecular cluster calculation, averaged over different configurations of the molecules in the first solvation shell), such calculations are very computationally demanding. Furthermore, cluster calculations typically do not afford accurate solvation energies, owing to the importance of longrange electrostatic interactions. Accurate prediction of solvation free energies is, however, crucial for modeling of chemical reactions and ligand/receptor interactions in solution.
QChem contains several different implicit solvent models, which differ greatly in their level of sophistication. These are generally known as selfconsistent reaction field (SCRF) models, because the continuum solvent establishes a “reaction field” (additional terms in the solute Hamiltonian) that depends upon the solute electron density, and must therefore be updated selfconsistently during the iterative convergence of the wave function. The simplest and oldest of these models that is available in QChem is the KirkwoodOnsager model,^{Kirkwood:1934, Onsager:1936, Kirkwood:1939} in which the solute molecule is placed inside of a spherical cavity and its electrostatic potential is represented in terms of a singlecenter multipole expansion. More sophisticated models, which use a moleculeshaped cavity and the full molecular electrostatic potential, include the conductorlike screening model^{Klamt:1993} (COSMO) and the closely related conductorlike PCM (CPCM),^{Truong:1995, Barone:1998, Cossi:2003} along with the “surface and simulation of volume polarization for electrostatics” [SS(V)PE] model.^{Chipman:2000} The latter is also known as the “integral equation formalism” (IEFPCM).^{Cances:1997, Cances:2001a}
The CPCM and IEFPCM/SS(V)PE are examples of what are called “apparent surface charge” SCRF models, although the term polarizable continuum models (PCMs), as popularized by Tomasi and coworkers,^{Tomasi:2005} is now used almost universally to refer to this class of solvation models. QChem employs a Switching/Gaussian or “SWIG” implementation of these PCMs.^{Lange:2010a, Lange:2010b, Lange:2011b, Herbert:2016a, Lange:2020} This approach resolves a longstanding—though littlepublicized—problem with standard PCMs, namely, that the boundaryelement methods used to discretize the solute/continuum interface may lead to discontinuities in the potential energy surface for the solute molecule. These discontinuities inhibit convergence of geometry optimizations, introduce serious artifacts in vibrational frequency calculations, and make ab initio molecular dynamics calculations virtually impossible.^{Lange:2010a, Lange:2010b} In contrast, QChem’s SWIG PCMs afford potential energy surfaces that are rigorously continuous and smooth. Unlike earlier attempts to obtain smooth PCMs, the SWIG approach largely preserves the properties of the underlying integralequation solvent models, so that solvation energies and molecular surface areas are hardly affected by the smoothing procedure.
Other solvent models available in QChem include the “Langevin dipoles” model;^{Florian:1997, Florian:1999} as well as versions 8 and 12 of the SM$x$ models, and the SMD model, developed at the University of Minnesota.^{Marenich:2007, Marenich:2013, Marenich:2009} SM8 and SM12 are based upon the generalized Born method for electrostatics, augmented with atomic surface tensions intended to capture nonelectrostatic effects (cavitation, dispersion, exchange repulsion, and changes in solvent structure). Empirical corrections of this sort are also available for the PCMs mentioned above, but within SM8 and SM12 these parameters have been optimized to reproduce experimental solvation energies. SMD (where the “D” is for “density") combines IEFPCM with the nonelectrostatic corrections, but because the electrostatics is based on the density rather than atomic point charges, it is supported for arbitrary basis sets whereas SM8 and SM12 are not.
Model  Cavity  Non  Supported  

Construction  Discretization  Electrostatic  Basis  
Terms?  Sets  
KirkwoodOnsager  spherical  point charges  no  all 
Langevin Dipoles  atomic spheres  dipoles in  no  all 
(userdefinable)  3d space  
CPCM  atomic spheres  point charges or  user  all 
(userdefinable)  smooth Gaussians  specified  
SS(V)PE/  atomic spheres  point charges or  user  all 
IEFPCM  (userdefinable)  smooth Gaussians  specified  
COSMO  predefined  point charges  none  all 
atomic spheres  
Isodensity SS(V)PE  isodensity contour  point charges  none  all 
SM8  predefined  generalized  automatic  631G* 
atomic spheres  Born  631+G*  
631+G**  
SM12  predefined  generalized  automatic  all 
atomic spheres  Born  
SMD  predefined  point charges  automatic  all 
atomic spheres  

Table 11.1 summarizes the implicit solvent models that are available in QChem. Solvent models are invoked via the SOLVENT_METHOD keyword, as shown below. Additional details about each particular solvent model can be found in the sections that follow. In general, these methods are available for any SCF level of electronic structure theory, though in the case of SM8 only certain basis sets are supported. PostHartree–Fock calculations can be performed by first running an SCF + PCM job, in which case the correlated wave function will employ MOs and HartreeFock energy levels that are polarized by the solvent.
Table 11.2 summarizes the analytical energy gradient and Hessian available with implicit solvent models. For unsupported methods, finite difference methods may be used for performing geometry optimizations and frequency calculations.
Energy Derivatives  CPCM  SS(V)PE/  COSMO  SM8  SM12  SMD 

IEFPCM  
SCF energy gradient  yes  yes  yes  yes  no  yes 
SCF energy Hessian  yes  no  yes  no  no  no 
CIS/TDDFT energy gradient  yes  no  — unsupported —  
CIS/TDDFT energy Hessian  yes  no  — unsupported —  
MP2 & DHDFT energy  — unsupported —  
derivatives  
Coupled cluster methods  — unsupported — 
Note: The jobcontrol format for specifying implicit solvent models changed significantly starting in QChem version 4.2.1. This change was made in an attempt to simply and unify the input notation for a large number of different models.
SOLVENT_METHOD
Sets the preferred solvent method.
TYPE:
STRING
DEFAULT:
0
OPTIONS:
0
Do not use a solvation model.
ONSAGER
Use the KirkwoodOnsager model (Section 11.2.1).
PCM
Use an apparent surface charge, polarizable continuum model
(Section 11.2.2).
ISOSVP
Use the isodensity implementation of the SS(V)PE model
(Section 11.2.5).
COSMO
Use COSMO (similar to CPCM but with an outlying charge
correction;^{Klamt:1996, Baldridge:1997} see
Section 11.2.7).
SM8
Use version 8 of the CramerTruhlar SM$x$ model (Section 11.2.8.1).
SM12
Use version 12 of the SM$x$ model (Section 11.2.8.2).
SMD
Use SMD (Section 11.2.8.3).
CHEM_SOL
Use the Langevin Dipoles model (Section 11.2.9).
RECOMMENDATION:
Consult the literature. PCM is a collective name for a family of models and
additional input options may be required in this case, in order to fully
specify the model. (See Section 11.2.2.) Several versions
of SM12 are available as well, as discussed in
Section 11.2.8.2.
Before going into detail about each of these models, a few potential points of confusion warrant mention, with regards to nomenclature. First, “PCM” refers to a family of models that includes CPCM and SS(V)PE/IEFPCM (the latter two being completely equivalent^{Cances:2001a}). One or the other of these models can be selected by additional job control variables in a $pcm input section, as described in Section 11.2.2. COSMO is very similar to CPCM but includes a correction for that part of the solute’s electron density that penetrates beyond the cavity (the socalled “outlying charge”).^{Klamt:1996, Baldridge:1997} This is discussed in Section 11.2.7.
Two implementations of the SS(V)PE model are also available. The PCM implementation (which is requested by setting SOLVENT_METHOD = PCM) uses a solute cavity constructed from atomcentered spheres, as with most other PCMs. On the other hand, setting SOLVENT_METHOD = ISOSVP requests an SS(V)PE calculation in which the solute cavity is defined by an isocontour of the solute’s own electron density, as advocated by Chipman.^{Chipman:2000, Chipman:2002a, Chipman:2002b} This is an appealing, oneparameter cavity construction, although it is unclear that this construction alone is superior in its accuracy to carefullyparameterized atomic radii,^{Barone:1997} at least not without additional, nonelectrostatic terms included,^{Pomogaeva:2011, Pomogaeva:2013, Pomogaeva:2014, Pomogaeva:2015} which are available in QChem’s implementation of the isodensity version of SS(V)PE (Section 11.2.6). Moreover, analytic energy gradients are not available for the isodensity cavity construction, whereas they are available when the cavity is constructed from atomcentered spheres. One additional subtlety, which is discussed in detail in Ref. Lange:2011b, is the fact that the PCM implementation of the equation for the SS(V)PE surface charges [Eq. (11.2)] uses an asymmetric $\mathbf{K}$ matrix. In contrast, Chipman’s isodensity implementation uses a symmetrized $\mathbf{K}$ matrix. Although the symmetrized version is somewhat more computationally efficient when the number of surface charges is large, the asymmetric version is better justified, theoretically.^{Lange:2011b} (This admittedly technical point is clarified in Section 11.2.2 and in particular in Table 11.3.)
Regarding the accuracy of these models for solvation free energies ($\mathrm{\Delta}{G}_{298}$), SM8 achieves subkcal/mol accuracy for neutral molecules, based on comparison to a large database of experimental values, although average errors for ions are more like 4 kcal/mol.^{Cramer:2008} To achieve comparable accuracy with IEFPCM/SS(V)PE, nonelectrostatic terms must be included.^{Klamt:2009, Pomogaeva:2011, Pomogaeva:2014} The SM12 model does not improve upon SM8 in any statistical sense,^{Marenich:2013} but does lift one important restriction on the level of electronic structure that can be combined with these models. Specifically, the Generalized Born model used in SM8 is based on a variant of Mullikenstyle atomic charges, and is therefore parameterized only for a few small basis sets, e.g., 631G*. SM12, on the other hand, uses a variety of charge schemes that are stable with respect to basisset expansion, and can therefore be combined with any level of electronic structure theory for the solute. Like IEFPCM, the SMD model is also applicable to any basis sets, and its accuracy is comparable to SM8 and SM12.^{Marenich:2009} Quantitative fluidphase thermodynamics can also be obtained using Klamt’s COSMORS approach,^{Klamt:1995, Klamt:2010} where RS stands for “real solvent”. The COSMORS approach is not included in QChem and requires the COSMOtherm program, which is licensed separately through COSMOlogic,^{COSMOlogic} but QChem can write the input files that are need by COSMOtherm.
The following sections provide more details regarding theory and job control for the various implicit solvent models that are available in QChem. In addition, recent review articles are available for PCM methods,^{Tomasi:2005} SM$x$,^{Cramer:2008} and COSMO.^{Klamt:2011} Formal relationships between various PCMs have been discussed in Refs. Chipman:2002a, Lange:2011b.