Continuum Solvation Methods In a very thorough 1994 review of continuum solvation models, Tomasi and Persico divide the possible approaches to the treatment of solvent effects into four categories: a) virial equations of state, correlation functions b) Monte Carlo or molecular dynamics simulations c) continuum treatments d) molecular treatments The Effective Fragment Potential method, documented in the following section of this chapter, falls into the latter category, as each EFP solvent molecule is modeled as a distinct object (discrete solvation). This section describes the four continuum models which are implemented in the standard version of GAMESS, and a fifth model which can be interfaced. Continuum models typically form a cavity of some sort containing the solute molecule, while the solvent outside the cavity is thought of as a continuous medium and is categorized by a limited amount of physical data, such as the dielectric constant. The electric field of the charged particles comprising the solute interact with this background medium, producing a polarization in it, which in turn feeds back upon the solute's wavefunction. Self Consistent Reaction Field (SCRF) A simple continuum model is the Onsager cavity model, often called the Self-Consistent Reaction Field, or SCRF model. This represents the charge distribution of the solute in terms of a multipole expansion. SCRF usually uses an idealized cavity (spherical or ellipsoidal) to allow an analytic solution to the interaction energy between the solute multipole and the multipole which this induces in the continuum. This method is implemented in GAMESS in the simplest possible fashion: i) a spherical cavity is used ii) the molecular electrostatic potential of the solute is represented as a dipole only, except a monopole is also included for an ionic solute. The input for this implementation of the Kirkwood-Onsager model is provided in $SCRF. Some references on the SCRF method are 1. J.G.Kirkwood J.Chem.Phys. 2, 351 (1934) 2. L.Onsager J.Am.Chem.Soc. 58, 1486 (1936) 3. O.Tapia, O.Goscinski Mol.Phys. 29, 1653 (1975) 4. M.M.Karelson, A.R.Katritzky, M.C.Zerner Int.J.Quantum Chem., Symp. 20, 521-527 (1986) 5. K.V.Mikkelsen, H.Agren, H.J.Aa.Jensen, T.Helgaker J.Chem.Phys. 89, 3086-3095 (1988) 6. M.W.Wong, M.J.Frisch, K.B.Wiberg J.Am.Chem.Soc. 113, 4776-4782 (1991) 7. M.Szafran, M.M.Karelson, A.R.Katritzky, J.Koput, M.C.Zerner J.Comput.Chem. 14, 371-377 (1993) 8. M.Karelson, T.Tamm, M.C.Zerner J.Phys.Chem. 97, 11901-11907 (1993) The method is very sensitive to the choice of the solute RADIUS, but not very sensitive to the particular DIELEC of polar solvents. The plots in reference 7 illustrate these points very nicely. The SCRF implementation in GAMESS is Zerner's Method A, described in the same reference. The total solute energy includes the Born term, if the solute is an ion. Another limitation is that a solute's electro- static potential is not likely to be fit well as a dipole moment only, for example see Table VI of reference 5 which illustrates the importance of higher multipoles. Finally, the restriction to a spherical cavity may not be very representative of the solute's true shape. However, in the special case of a roundish molecule, and a large dipole which is geometry sensitive, the SCRF model may include sufficient physics to be meaningful: M.W.Schmidt, T.L.Windus, M.S.Gordon J.Am.Chem.Soc. 117, 7480-7486(1995). Most cases should choose PCM (next section) over SCRF!!! Polarizable Continuum Model (PCM) A much more sophisticated continuum method, named the Polarizable Continuum Model, is also available. The PCM method places a solute in a cavity formed by a union of spheres centered on each atom. PCM includes a more exact treatment of the electrostatic interaction of the solute with the surrounding medium, on the cavity's surface. The computational procedure divides this surface into many small tesserae, each having a different "apparent surface charge", reflecting the solute's and other tesserae's electric field at each. These surface charges are the PCM model's "solvation effect" and make contributions to the energy and to the gradient of the solute. Typically the cavity is defined as a union of atomic spheres, which should be roughly 1.2 times the atomic van der Waals radii. A technical difficulty caused by the penetration of the solute's charge density outside this cavity is dealt with by a renormalization. The solvent is characterized by its dielectric constant, surface tension, size, density, and so on. Procedures are provided not only for the computation of the electrostatic interaction of the solute with the apparent surface charges, but also for the cavitation energy, and for the dispersion and repulsion contributions to the solvation free energy. Methodology for solving the Poisson equation to obtain the "apparent surface charges" has progressed from D-PCM to IEF-PCM to C-PCM over time, with the latter preferred. Iterative solvers require far less computer resources than direct solvers. Advancements have also been made in schemes to divide the surface cavity into tiny tesserae. As of fall 2008, the FIXPVA tessellation, which has smooth switching functions for tesserae near sphere boundaries, together with iterative C-PCM, gives very satisfactory geometry optimizations for molecules of 100 atoms. The FIXPVA tessellation was extended to work for cavitation (ICAV), dispersion (IDP), and repulsion (IREP) options in fall 2009, and dispersion/repulsion (IDISP) in spring 2010. Other procedures remain, and make the input seem complex, but their use is discouraged. Thus $PCM SOLVNT=WATER $END chooses iterative C-PCM (IEF=-10) and FIXPVA tessellation (METHOD=4 in $TESCAV) to do basic electrostatics in an accurate fashion. The main input group is $PCM, with $PCMCAV providing auxiliary cavity information. If any of the optional energy computations are requested in $PCM, the additional input groups $IEFPCM, $NEWCAV, $DISBS, or $DISREP may be required. It is useful to summarize the various cavities used by PCM, since as many as three cavities may be used: the basic cavity for electrostatics, cavity for cavitation energy, if ICAV=1, cavity for dispersion/repulsion, if IDISP=1. The first and second share the same radii (see RADII in $PCMCAV), which are scaled by ALPHA=1.2 for electrostatics, but are used unscaled for cavitation. The dispersion cavity is defined in $DISREP with a separate set of atomic radii, and even solvent molecule radii! Only the electrostatics cavity can use any of the GEPOL-GB, GEPOL-AS or recommended FIXPVA tessellation, while the other two use only the original GEPOL-GB. Radii are an important part of the PCM parameterization. Their values can have a significant impact on the quality of the results. This is particularly true if the solute is charged, and thus has a large electrostatic interaction with the continuum. John Emsley's book "The Elements" is a useful source of van der Waals and other radii. PCM is at heart a means of treating the electrostatic interactions between the solute's wavefunction and a dielectric model for the bulk solvent. The former is represented as an electron density from whatever quantum mechanical treatment is used for the solute, and the latter is a set of surface charges on the finite elements of the cavity (tessellation). This leaves out other important contributions to the solvation energy! These include the energy needed to make a hole in the solvent (cavitation energy), dispersion or repulsive interactions between the solute and solvent, and in the SMD model (see below) solvent structure changes such as would occur in the first solvation shell. Some empirical formulae for such "CDS" corrections are provided as keywords ICAV, IDISP, IREP/IDP, which may not work with all wavefunctions, and may not be compatible with gradients. The SMD model gives an alternative set of such "CDS" corrections, which are compatible with nuclear gradients: see SMD=.TRUE. in $PCM. A more detailed description of SMD is given in the paper cited below. The SMD solvent parameters is described (as of 2010) in http://comp.chem.umn.edu/solvation/mnsddb.pdf This gives numerical parameters, all built into GAMESS, as the various SOLX values, for SOLVNT= ACETACID CLPROPAN PHOPH EGME E2PENTEN ACETONE OCLTOLUE DPROAMIN MEACETAT PENTACET ACETNTRL M-CRESOL DODECAN MEBNZATE PENTAMIN ACETPHEN O-CRESOL MEG MEBUTATE PFB ANILINE CYCHEXAN ETSH MEFORMAT BENZALCL ANISOLE CYCHEXON ETHANOL MIBK PROPANAL BENZALDH CYCPENTN ETOAC MEPROPYL PROPACID BENZENE CYCPNTOL ETOME ISOBUTOL PROPANOL BENZNTRL CYCPNTON EB TERBUTOL PROPNOL2 BENZYLCL DECLNCIS PHENETOL NMEANILN PROPNTRL BRISOBUT DECLNTRA C6H5F MECYCHEX PROPENOL BRBENZEN DECLNMIX FOCTANE NMFMIXTR PROPACET BRETHANE DECANE FORMAMID ISOHEXAN PROPAMIN BROMFORM DECANOL FORMACID MEPYRID2 PYRIDINE BROCTANE EDB12 HEPTANE MEPYRID3 C2CL4 BRPENTAN DIBRMETN HEPTANOL MEPYRID4 THF BRPROPA2 BUTYLETH HEPTNON2 C6H5NO2 SULFOLAN BRPROPAN ODICLBNZ HEPTNON4 C2H5NO2 TETRALIN BUTANAL EDC12 HEXADECN CH3NO2 THIOPHEN BUTACID C12DCE HEXANE NTRPROP1 PHSH BUTANOL T12DCE HEXNACID NTRPROP2 TOLUENE BUTANOL2 DCM HEXANOL ONTRTOLU TBP BUTANONE ETHER HEXANON2 NONANE TCA111 BUTANTRL ET2S HEXENE NONANOL TCA112 BUTILE DIETAMIN HEXYNE NONANONE TCE NBA MI C6H5I OCTANE ET3N NBUTBENZ DIPE IOBUTANE OCTANOL TFE222 SBUTBENZ DMDS C2H5I OCTANON2 TMBEN124 TBUTBENZ DMSO IOHEXDEC PENTDECN ISOCTANE CS2 DMA CH3I PENTANAL UNDECANE CARBNTET CISDMCHX IOPENTAN NPENTANE M-XYLENE CLBENZEN DMF IOPROPAN PENTACID O-XYLENE SECBUTCL DMEPEN24 CUMENE PENTANOL P-XYLENE CHCL3 DMEPYR24 P-CYMENE PENTNON2 XYLENEMX CLHEXANE DMEPYR26 MESITYLN PENTNON3 CLPENTAN DIOXANE METHANOL PENTENE and provides a translation table to full chemical names, if you can't guess from the input choices given above. The translations can also be found in the source code. Two important things to note about SMD are: a) the atomic radii are changed, so although the algorithms for electrostatics are those of standard PCM, the numerical results for the electrostatics do change. b) SMD's parameterization was developed for IEF-PCM using GEPOL tessellation with a fine grid: IEF=-3 and MTHALL=2, NTSALL=240. However it is considered acceptable to use SMD's parameters, unchanged, with C-PCM and with the FIXPVA tessellation, at default coarseness. Hence, input such as $pcm solvnt=dmso smd=.true. $end is enough to carry out a SMD-style C-PCM treatment in DMSO. c) The CDS correction involves cavitation, dispersion, and as a collective "solvent structure contribution" estimates for partial hydrogen bonding, repulsion, and deviation of the dielectric constant from its bulk value. d) See also SMVLE in the more sophisticated SS(V)PE continuum model's description. Solvation of course affects the non-linear optical properties of molecules. The PCM implementation extends RUNTYP=TDHF to include solvent effects. Both static and frequency dependent hyperpolarizabilities can be found. Besides the standard PCM electrostatic contribution, the IREP and IDP keywords can be used to determine the effects of repulsion and dispersion on the polarizabilities. The implementation of the PCM model in GAMESS has received considerable attention from Hui Li and Jan Jensen at the University of Iowa, Iowa State University, and University of Nebraska. This includes new iterative techniques to solving the surface charge problem, new tessellations that provide for numerically stable nuclear gradients, the implementation of C-PCM equations, the extension of PCM to all SCFTYPs and TDDFT, development of an interface with the EFP model (quo vadis), and heterogenous dielectric. Dmitri Fedorov at AIST has interfaced PCM to the FMO method (quo vadis), and reduced storage requirements. Due to its sophistication, users of the PCM model are strongly encouraged to read the primary literature: Of particular relevance to PCM in GAMESS: 1) "Continuum solvation of large molecules described by QM/MM: a semi-iterative implementation of the PCM/EFP interface" H.Li, C.S.Pomelli, J.H.Jensen Theoret.Chim.Acta 109, 71-84(2003) 2) "Improving the efficiency and convergence of geometry optimization with the polarizable continuum model: new energy gradients and molecular surface tessellation" H.Li, J.H.Jensen J.Comput.Chem. 25, 1449-1462(2004) 3) "The polarizable continuum model interfaced with the Fragment Molecular Orbital method" D.G.Fedorov, K.Kitaura, H.Li, J.H.Jensen, M.S.Gordon J.Comput.Chem. 27, 976-985(2006) 4) "Energy gradients in combined Fragment Molecular Orbital and Polarizable Continuum Model (FMO/PCM)" H.Li, D.G.Fedorov, T.Nagata, K.Kitaura, J.H.Jensen, M.S.Gordon J.Comput.Chem. 31, 778-790(2010) 5) "Continuous and smooth potential energy surface for conductor-like screening solvation model using fixed points with variable area" P.Su, H.Li J.Chem.Phys. 130, 074109/1-13(2009) 6) "Heterogenous conductorlike solvation model" D.Si, H.Li J.Chem.Phys. 131, 044123/1-8(2009) 7) "Quantum mechanical/molecular mechanical/continuum style solvation model: linear response theory, variational treatment, and nuclear gradients" H.Li J.Chem.Phys. 131, 184103/1-8(2009) 8) "Smooth potential energy surface for cavitation, dispersion, and repulsion free energies in polarizable continuum model" Y.Wang, H.Li J.Chem.Phys. 131, 206101/1-2(2009) 9) "Excited state geometry of photoactive yellow protein chromophore: a combined conductorlike polarizable continuum model and time-dependent density functional study" Y.Wang, H.Li J.Chem.Phys. 133, 034108/1-11(2010) Paper number 7 is about the treatment of QM systems with the solvation models EFP and/or C-PCM. SMD and its CDS cavitation/dispersion/solvent structure corrections are described in "Universal solution model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions" A.V.Marenich, C.J.Cramer, D.G.Truhlar J.Phys.Chem.B 113, 6378-6396(2009) General papers on PCM: 10) S.Miertus, E.Scrocco, J.Tomasi Chem.Phys. 55, 117-129(1981) 11) J.Tomasi, M.Persico Chem.Rev. 94, 2027-2094(1994) 12) R.Cammi, J.Tomasi J.Comput.Chem. 16, 1449-1458(1995) 13) J.Tomasi, B.Mennucci, R.Cammi Chem.Rev. 105, 2999-3093(2005) The GEPOL-GB method for cavity construction: 14) J.L.Pascual-Ahuir, E.Silla, J.Tomasi, R.Bonaccorsi J.Comput.Chem. 8, 778-787(1987) Charge renormalization (see also ref. 12): 15) B.Mennucci, J.Tomasi J.Chem.Phys. 106, 5151-5158(1997) Derivatives with respect to nuclear coordinates: (energy gradient and hessian) See also paper 2 and 3. 16) R.Cammi, J.Tomasi J.Chem.Phys. 100, 7495-7502(1994) 17) R.Cammi, J.Tomasi J.Chem.Phys. 101, 3888-3897(1995) 18) M.Cossi, B.Mennucci, R.Cammi J.Comput.Chem. 17, 57-73(1996) Derivatives with respect to applied electric fields: (polarizabilities and hyperpolarizabilities) 19) R.Cammi, J.Tomasi Int.J.Quantum Chem. Symp. 29, 465-474(1995) 20) R.Cammi, M.Cossi, J.Tomasi J.Chem.Phys. 104, 4611-4620(1996) 21) R.Cammi, M.Cossi, B.Mennucci, J.Tomasi J.Chem.Phys. 105, 10556-10564(1996) 22) B. Mennucci, C. Amovilli, J. Tomasi Chem.Phys.Lett. 286, 221-225(1998) Cavitation energy: 23) R.A.Pierotti Chem.Rev. 76, 717-726(1976) 24) J.Langlet, P.Claverie, J.Caillet, A.Pullman J.Phys.Chem. 92, 1617-1631(1988) Dispersion and repulsion energies: 25) F.Floris, J.Tomasi J.Comput.Chem. 10, 616-627(1989) 26) C.Amovilli, B.Mennucci J.Phys.Chem.B 101, 1051-1057(1997) Integral Equation Formalism PCM. The first of these deals with anisotropies, the last 2 with nuclear gradients. 27) E.Cances, B.Mennucci, J.Tomasi J.Chem.Phys. 107, 3032-3041(1997) 28) B.Mennucci, E.Cances, J.Tomasi J.Phys.Chem.B 101, 10506-17(1997) 29) B.Mennucci, R.Cammi, J.Tomasi J.Chem.Phys. 109, 2798-2807(1998) 30) J.Tomasi, B.Mennucci, E.Cances J.Mol.Struct.(THEOCHEM) 464, 211-226(1999) 31) E.Cances, B.Mennucci J.Chem.Phys. 109, 249-259(1998) 32) E.Cances, B.Mennucci, J.Tomasi J.Chem.Phys. 109, 260-266(1998) Conductor PCM (C-PCM): 33) V.Barone, M.Cossi J.Phys.Chem.A 102, 1995-2001(1998) 34) M.Cossi, N.Rega, G.Scalmani, V.Barone J.Comput.Chem. 24, 669-681(2003) C-PCM with TD-DFT: 35) M.Cossi, V.Barone J.Chem.Phys. 115, 4708-4717(2001) See also paper #8 above for the coding in GAMESS. At the present time, the PCM model in GAMESS has the following limitations: a) Any SCFTYP may be used (RHF to MCSCF). MP2 or DFT may be used with any of the RHF, UHF, and ROHF gradient programs. Closed shell TD-DFT excited state gradients may also be used. CI and Coupled Cluster programs are not available. b) semi-empirical methods may not be used. c) the only other solvent method that may be used at used with PCM is the EFP model. d) point group symmetry is switched off internally during PCM. e) The PCM model runs in parallel for IEF=3, -3, 10, or -10 and for all 5 wavefunctions (energy or gradient), but not for RUNTYP=TDHF jobs. f) D-PCM stores electric field integrals at normals to the surface elements on disk. IEF-PCM and C-PCM using the explicit solver (+3 and +10) store electric potential integrals at normals to the surface on disk. This is true even for direct AO integral runs, and the file sizes may be considerable (basis set size squared times the number of tesserae). IEF-PCM and C-PCM with the iterative solvers do not store the potential integrals, when IDIRCT=1 in the $PCMITR group (this is the default) g) nuclear derivatives are limited to gradients, although theory for hessians is given in paper 17. * * * The only PCM method prior to Oct. 2000 was D-PCM, which can be recovered by selecting IEF=0 and ICOMP=2 in $PCM. The default PCM method between Oct. 2000 and May 2004 was IEF-PCM, recoverable by IEF=-3 (but 3 for non-gradient runs) and ICOMP=0. As of May 2004, the default PCM method was changed to C-PCM (IEF=-10, ICOMP=0). The extension of PCM to all SCFTYPs as of May 2004 involved a correction to the MCSCF PCM operator, so that it would reproduce RHF results when run on one determinant, meaning that it is impossible to reproduce prior MCSCF PCM calculations. The cavity definition was GEPOL-GB (MTHALL=1 in $TESCAV) prior to May 2004, GEPOL-AS (MTHALL=2) from then until September 2008, and FIXPVA (MTHALL=4) to the present time. The option for generation of 'extra spheres' (RET in $PCM) was changed from 0.2 to 100.0, to suppress these, in June 2003. * * * In general, use of PCM electrostatics is very simple, as may be seen from exam31.inp supplied with the program. The calculation shown next illustrates the use of some of the older PCM options. Since methane is non-polar, its internal energy change and the direct PCM electrostatic interaction is smaller than the cavitation, repulsion, and dispersion corrections. Note that the use of ICAV, IREP, and IDP are currently incompatible with gradients, so a reasonable calculation sequence might be to perform the geometry optimization with PCM electrostatics turned on, then perform an additional calculation to include the other solvent effects, adding extra functions to improve the dispersion correction. ! calculation of CH4 (metano), in PCM water. ! ! This input reproduces the data in Table 2, line 6, of ! C.Amovilli, B.Mennucci J.Phys.Chem.B 101, 1051-7(1997) ! To do this, we must use many original PCM options. ! ! The gas phase FINAL energy is -40.2075980292 ! The FINAL energy in PCM water is -40.2048210283 ! (lit.) ! FREE ENERGY IN SOLVENT = -25234.89 KCAL/MOL ! INTERNAL ENERGY IN SOLVENT = -25230.64 KCAL/MOL ! DELTA INTERNAL ENERGY = .01 KCAL/MOL ( 0.0) ! ELECTROSTATIC INTERACTION = -.22 KCAL/MOL (-0.2) ! PIEROTTI CAVITATION ENERGY = 5.98 KCAL/MOL ( 6.0) ! DISPERSION FREE ENERGY = -6.00 KCAL/MOL (-6.0) ! REPULSION FREE ENERGY = 1.98 KCAL/MOL ( 2.0) ! TOTAL INTERACTION = 1.73 KCAL/MOL ( 1.8) ! TOTAL FREE ENERGY IN SOLVENT= -25228.91 KCAL/MOL ! $contrl scftyp=rhf runtyp=energy $end $guess guess=huckel $end $system mwords=2 $end ! the "W1 basis" input here exactly matches HONDO's DZP $DATA CH4...gas phase geometry...in PCM water Td Carbon 6. DZV D 1 ; 1 0.75 1.0 Hydrogen 1. 0.6258579976 0.6258579976 0.6258579976 DZV 0 1.20 1.15 ! inner and outer scale factors P 1 ; 1 1.00 1.0 $END ! The reference cited used a value for H2O's solvent ! radius that differs from the built in value (RSOLV). ! The IEF, ICOMP, MTHALL, and RET keywords are set to ! duplicate the original code's published results, ! namely D-PCM and GEPOL-GB. This run doesn't put in ! any "extra spheres" but we try that option (RET) ! like it originally would have. $PCM SOLVNT=WATER RSOLV=1.35 RET=0.2 IEF=0 ICOMP=2 IDISP=0 IREP=1 IDP=1 ICAV=1 $end $TESCAV MTHALL=1 $END $NEWCAV IPTYPE=2 ITSNUM=540 $END ! dispersion "W2 basis" uses exponents which are ! 1/3 of smallest exponent in "W1 basis" of $DATA. $DISBS NADD=11 NKTYP(1)=0,1,2, 0,1, 0,1, 0,1, 0,1 XYZE(1)=0.0,0.0,0.0, 0.0511 0.0,0.0,0.0, 0.0382 0.0,0.0,0.0, 0.25 1.1817023, 1.1817023, 1.1817023, 0.05435467 1.1817023, 1.1817023, 1.1817023, 0.33333333 -1.1817023, 1.1817023,-1.1817023, 0.05435467 -1.1817023, 1.1817023,-1.1817023, 0.33333333 1.1817023,-1.1817023,-1.1817023, 0.05435467 1.1817023,-1.1817023,-1.1817023, 0.33333333 -1.1817023,-1.1817023, 1.1817023, 0.05435467 -1.1817023,-1.1817023, 1.1817023, 0.33333333 $end SVPE and SS(V)PE. The Surface Volume Polarization for Electrostatics (SVPE), and an approximation to SVPE called the Surface and Simulation of Volume Polarization for Electrostatics (SS(V)PE) are continuum solvation models. Compared to other continuum models, SVPE and SS(V)PE pay careful attention to the problems of escaped charge, the shape of the surface cavity, and to integration of the Poisson equation for surface charges. The original references for what is now called the SVPE (surface and volume polarization for electrostatics) method are the theory paper: "Charge penetration in Dielectric Models of Solvation" D.M.Chipman, J.Chem.Phys. 106, 10194-10206 (1997) and two implementation papers: "Volume Polarization in Reaction Field Theory" C.-G.Zhan, J.Bentley, D.M.Chipman J.Chem.Phys. 108, 177-192 (1998) "New Formulation and Implementation for Volume Polarization in Dielectric Continuum Theory" D.M.Chipman, J.Chem.Phys. 124, 224111-1/10 (2006) which should be cited in any publications that utilize the SVPE code. There are two options to include with SS(V)PE or SVPE additional models that describe short-range solute-solvent interactions to achieve a more complete description of solvation energies. Both have their keywords merged into the $SVP input group for convenience. One option to include short-range interactions is CMIRS1.0 (Composite Method for Implicit Representation of Solvent, Version 1.0) that combines the SS(V)PE dielectric continuum model with the DEFESR (Dispersion, Exchange, and Field-Extremum Short- Range) model. A complete account of CMIRS1.0 with application to hydration energies is given in: ?Hydration Energy from a Composite Method for Implicit Representation of Solvent? A.Pomogaeva, D.M.Chipman J.Chem.Theory Comput. 10, 211-219(2014) which should be referenced in any publication that uses the model. References to earlier works that develop the individual components of the DEFESR parts of the full CMIRS recipe are: ?Modeling short-range contributions to hydration energies with minimal parameterization? A.Pomogaeva, D.W.Thompson, and D.M.Chipman Chem.Phys.Lett. 511, 161-165(2011). ?Field-Extremum Model for Short-Range Contributions to Hydration Free Energy? A.Pomogaeva and D.M.Chipman J.Chem.Theory Comput. 7, 3952-3960(2011). ?New Implicit Solvation Models for Dispersion and Exchange Energies? A.Pomogaeva and D.M.Chipman J.Phys.Chem.A, 117, 5812-5820 (2013). The other option to include short-range interactions is the SMVLE (solvation model with volume and local electrostatics) as described in "Free energies of solvation with surface, volume, and local electrostatic effects and atomic surface tensions to represent the first solvation shell" J.Liu, C.P.Kelly, A.C.Goren, A.V.Marenich, C.J.Cramer, D.G.Truhlar, C.-G. Zhan J.Chem.Theory Comput. 6, 1109-1117(2010). Further information on the performance of SVPE and of SS(V)PE can be found in: "Comparison of Solvent Reaction Field Representations" D.M.Chipman, Theor.Chem.Acc. 107, 80-89 (2002). Details of the SS(V)PE convergence behavior and programming strategy are in: "Implementation of Solvent Reaction Fields for Electronic Structure" D.M.Chipman, M.Dupuis, Theor.Chem.Acc. 107, 90-102 (2002). The SMVLE option (solvation model with volume and local electrostatics) is described in "Free energies of solvation with surface, volume, and local electrostatic effects and atomic surface tensions to represent the first solvation shell" J.Liu, C.P.Kelly, A.C.Goren, A.V.Marenich, C.J.Cramer, D.G.Truhlar, C.-G. Zhan J.Chem.Theory Comput. 6, 1109-1117(2010). The SVPE and SS(V)PE models are like PCM and COSMO in that they treat solvent as a continuum dielectric residing outside a molecular-shaped cavity, determining the apparent charges that represent the polarized dielectric by solving Poisson's equation. The main difference between SVPE and SS(V)PE is in treatment of volume polarization effects that arise because of the tail of the electronic wave function that penetrates outside the cavity, sometimes referred to as the "escaped charge." SVPE treats volume polarization effects explicitly by including apparent charges in the volume outside the cavity as well as on the cavity surface. With a sufficient number of grid points, SVPE can then provide an exact treatment of charge penetration effects. SS(V)PE, like PCM and COSMO, is an approximate treatment that only uses apparent charges located on the cavity surface. The SS(V)PE equation is particularly designed to simulate as well as possible the influence of the missing volume charges. For more information on the similarities and differences of the SVPE and SS(V)PE models with other continuum methods, see the paper "Comparison of Solvent Reaction Field Representations" cited just above. In addition, the cavity construction and Poisson solver used in this implementation of SVPE and SS(V)PE also receive careful numerical treatment. For example, the cavity may be chosen to be an isodensity contour surface, and the Lebedev grids for the Poisson solver can be chosen very densely. The Lebedev grids used for surface integration are taken from the Fortran translation by C. van Wuellen of the original C programs developed by D. Laikov. They were obtained from the CCL web site www.ccl.net/cca/software/SOURCES/FORTRAN/Lebedev-Laikov- Grids. A recent leading reference is V. I. Lebedev and D. N. Laikov, Dokl. Math. 59, 477-481 (1999). All these grids have octahedral symmetry and so are naturally adapted for any solute having an Abelian point group. The larger and/or the less spherical the solute may be, the more surface points are needed to get satisfactory precision in the results. Further experience will be required to develop detailed recommendations for this parameter. Values as small as 110 are usually sufficient for simple diatomics and triatomics. The default value of 1202 has been found adequate to obtain the energy to within 0.1 kcal/mol for solutes the size of monosubstituted benzenes. The SVPE method uses additional layers of points outside the cavity. Typically just two layers are sufficient to converge the direct volume polarization contribution to better than 0.1 kcal/mol. The SVPE and SS(V)PE codes both report the amount of solute charge penetrating outside the cavity as calculated by Gauss' Law. The SVPE code additionally reports the same quantity as alternatively calculated from the explicit volume charges, and any substantial discrepancy between these two determinations indicates that more volume polarization layers should have been included for better precision. The energy contribution from the outermost volume polarization layer is also reported. If it is significant then again more layers should have been included. However, these tests are only diagnostic. Passing them does not guarantee that enough layers are included. The SVPE and SS(V)PE models treat the electrostatic interaction between a quantum solute and a classical dielectric continuum solvent. No treatment is yet implemented for cavitation, dispersion, or any of a variety of other specific solvation effects. Note that corrections for these latter effects that might be reported by other programs are generally not transferable. The reason is that they are usually parameterized to improve the ultimate agreement with experiment. In addition to providing corrections for the physical effects advertised, they therefore also inherently include contributions that help to make up for any deficiencies in the electrostatic description. Consequently, they are appropriate only for use with the particular electrostatic model in which they were originally developed. Analytic nuclear gradients are not yet available for the SVPE or SS(V)PE energy, but numerical differentiation will permit optimization of small solute molecules. Wavefunctions may be any of the SCF type: RHF, UHF, ROHF, GVB, and MCSCF, or the DFT analogs of some of these. In the MCSCF implementation, no initial wavefunction is available so the solvation code does not kick in until the second iteration. We close with a SVPE example. The gas phase energy, obtained with no $SVP group, is -207.988975, and the run just below gives the SVPE energy -208.006282. The free energy of solvation, -10.860 kcal/mole, is the difference of these, and is quoted at the right side of the 3rd line from the bottom of Table 2 in the paper cited. The "REACTION FIELD FREE ENERGY" for SVPE is -12.905 kcal/mole, which is only part of the solvation free energy. There is also a contribution due to the SCRF procedure polarizing the wave function from its gas phase value, causing the solute internal energy in dielectric to differ from that in gas. Evaluating this latter contribution is what requires the separate gas phase calculation. Changing the number of layers (NVLPL) to zero produces the SS(V)PE approximation to SVPE, E= -208.006208. ! SVPE solvation test...acetamide ! reproduce data in Table 2 of the paper on SVPE, ! D.M.Chipman J.Chem.Phys. 124, 224111/1-10(2006) ! $contrl scftyp=rhf runtyp=energy $end $system mwords=4 $end $basis gbasis=n31 ngauss=6 ndfunc=1 npfunc=1 $end $guess guess=moread norb=16 $end $scf nconv=8 $end $svp nvlpl=3 rhoiso=0.001 dielst=78.304 nptleb=1202 $end $data CH3CONH2 cgz geometry RHF/6-31G(d,p) C1 C 6.0 1.361261 -0.309588 -0.000262 C 6.0 -0.079357 0.152773 -0.005665 H 1.0 1.602076 -0.751515 0.962042 H 1.0 1.537200 -1.056768 -0.767127 H 1.0 2.002415 0.542830 -0.168045 O 8.0 -0.387955 1.310027 0.002284 N 7.0 -1.002151 -0.840834 -0.011928 H 1.0 -1.961646 -0.589397 0.038911 H 1.0 -0.752774 -1.798630 0.035006 $end gas phase vectors, E(RHF)= -207.9889751769 $VEC 1 1 1.18951670E-06 1.74015997E-05 ...snipped... $END The example just above can be changed to a CMIRS run, by changing NVLPL to zero and also requesting calculation of the DEFESR contributions. The result should be a CMIRS1.0 total free energy of -208.013517. The input should (1) in $CONTRL, specify DFTTYP=HFX, which requests a Hartree-Fock calculation, but sets up DFT grids, (2) in $DFT, request a very accurate grid $dft method=grid nrad=96 nleb=1202 nrad0=96 nleb0=1202 $end (3) in $SVP, invoke the keyword IDEF=1. Adding the keyword EGAS=-207.9889751769 to any of these examples allows reporting of the free energy of solvation (-10.860 kcal/mol for SVPE, -10.814 for SS(V)PE, -15.400 for CMIRS1.0). Conductor-like screening model (COSMO) The COSMO (conductor-like screening model) represents a different approach for carrying out polarized continuum calculations. COSMO was originally developed by Andreas Klamt, with extensions to ab initio computation in GAMESS by Kim Baldridge. In the COSMO method, the surrounding medium is modeled as a conductor rather than as a dielectric in order to establish the initial boundary conditions. The assumption that the surrounding medium is well modeled as a conductor simplifies the electrostatic computations and corrections may be made a posteriori for dielectric behavior. The original model of Klamt was introduced using a molecular shaped cavity, which had open parts along the crevices of intersecting atomic spheres. While having considerable technical advantages, this approximation causes artifacts in the context of the more generalized theory, so the current method for cavity construction includes a closure of the cavity to eliminate crevices or pockets. Two methodologies are implemented for treatment of the outlying charge errors (OCE). The default is the well- established double cavity procedure using a second, larger cavity around the first one, and calculates OCE through the difference between the potential on the inner and the outer cavity. The second involves the calculation of distributed multipoles up to hexadecapoles to represent the entire charge distribution of the molecule within the cavity. The COSMO model accounts only for the electrostatic interactions between solvent and solute. Klamt has proposed a novel statistical scheme to compute the full solvation free energy for neutral solutes, COSMO-RS, which is formulated for GAMESS by Peverati, Potier and Baldridge, and is available as external plugin to the COSMOtherm program by COSMOlogic GmbH&Co. The iterative inclusion of non-electrostatic effects is also possible right after a COSMO-RS calculation. The DCOSMO-RS approach was implemented in GAMESS by Peverati, Potier, and Baldridge, and more information is available on Baldridge website at: http://ocikbws.uzh.ch/gamess/ The simplicity of the COSMO model allows computation of gradients, allowing optimization within the context of the solvent. The method is programmed for RHF and UHF, all corresponding kinds of DFT (including DFT-D), and the corresponding MP2, energy and gradient. Some references on the COSMO model are: A.Klamt, G.Schuurman J.Chem.Soc.Perkin Trans 2, 799-805(1993) A.Klamt J.Phys.Chem. 99, 2224-2235(1995) K.Baldridge, A.Klamt J.Chem.Phys. 106, 6622-6633 (1997) V.Jonas, K.Baldridge J.Chem.Phys. 113, 7511-7518 (2000) L.Gregerson, K.Baldridge Helv.Chim.Acta 86, 4112-4132 (2003) R.Peverati, Y.Potier, K.Baldridge TO BE PUBLISHED SOON Additional references on the COSMO-RS model, with explanation of the methodology and program can be found: A.Klamt, F.Eckert, W.Arlt Annu.Rev.Chem.Biomol.Eng. 1, (2010)