Presentation on theme: "Continuum Solvation Models in Gaussian 03"— Presentation transcript:
1 Continuum Solvation Models in Gaussian 03 Dr. Ivan RostovAustralian National University,Canberra
2 Outline Types of solvent effects and solvent models Overview of solvation continuum models available in Gaussian 03.Summary of Gaussian keywordsApplicationsRecommendationsIn my talk I am going to give you a brief introduction to the theory of solvation continuum models available in Gaussian 03. I give you examples of keywords to setup Gaussian solvation calculations and demonstrate their efficiency of the continuum approach on a few examples. At the end of the talk I give you some recommendations which might be useful for Gaussian users, who just about to start calculations using continuum solvation models. Hopefully, they will be of help to minimize your computation costs.
3 Solvent EffectsNicolai Alexandrovich Menshutkin, Z. Physik. Chem. 1890, 5, 589NH3 CH3Cl NH3CH3+ Cl-The fact that solvent may affect the properties of chemical substances has been known for centuries. However, it was only in the second half of 19th century, with rise of the atomistic theory of matter, when people started to understand that the solvent effects is not a magic but can be explained solely by science. In 1890, the head of recently born Russian Chemical Society Nikolai Menshutkin published a paper on the effect of polarity of solvent on the rate of what we know now as Menshutkin reaction. Nowadays, it is common name for the reaction of methylation of tertiary amines to quaternary ammonium salt by alkyl halide. In simple case we have neutral ammonia and methyl chloride on input and ions of methylammonium chloride salt on output. Menshutkin found in his experiment that the rate and endothermithicity, or exothermicity of reaction changes with the polarity of the solvent. As found, the problem can be brought to taking the proper accounting of physical interactions between solute and solvent molecules. This discovery was giving a sign that the electrostatic forces induced between solute and solvent molecules play the major role behind the solvent effects.
4 Solvent Effects The solvent environment influences all of these: StructureEnergiesReaction and activation energiesBond energiesSpectraRotational (Microwave)Vibrational (IR, Raman)Electronic (UV, visible)To the present day, it was found that the solvent environment influences structure, energies, spectra and other properties of solute. Therefore, they must be taken into account in Computational Chemistry when we modelling reaction in realistic environment.
5 Methods for Treatment of Solvation SupermoleculeSolute and some number of solvent molecules are included in one large QM calculationMolecular Mechanics Force FieldsSimple classical force fields allows us to include a large number of solvent moleculesContinuum modelsExplicit consideration of solvent molecules is neglectedSolvent effects are described in terms of macroscopic properties of the chosen solvent (e, <Rsolvent>)Hybrid/mixed:Supermolecule + Continuum modelQM + MMQM + MM + Continuum modelThe major approaches in Computational Chemistry in treating of solvent effects are:supermolecule, continuum models, Molecular Mechanics, and recently appeared various hybrid constructions.In the supermolecule approach one places some number of solvent molecules together with solute in the one QM calculation. While, in many cases, it can give some insights on solvent effects even with limited number of solvent molecules, the quantitative results require the very large of number of solvent molecules to be included brining the computational costs beyond the present day limits.Molecular Mechanics methods due to the simplicity of the atom-atomic force field allows us take quite a reasonable number of solvent molecules into consideration at cheap price. However, the simplicity of the MM approach does not allow the MM methods to get an adequate description of many processes, such as bond breaking in chemical reaction, for example. Regarding of the solvent effects, the accounting for the mutual polarization of solute and solvent molecules requires a considerable complication of the MM theory rising considerably the cost of such calculations.The hybrid QM/MM methods is quite a fresh branch on the tree of Computational Chemistry. It is a promising approach. However, QM/MM calculations are not easy to setup and they are costly.Now we come to continuum solvation models. To the surprise of many sceptical opponents, the combination of QM methods with continuum solvation theory proven to be a successful. Surely, it has limitation on area of applicability, but where it works it allows us to get an estimate of solvent effects at quite a cheap price. The cheap price is achieved by exclusion of information on explicit configuration of solvent molecules. Solvent is described as a uniform medium characterized by some macroscopic properties.(Add pictures) Talk small add some subbullet
6 Solvation Process 2) Turning on dispersion and repulsion forces 3) Turning on electrostatic forces1) Creation of cavityFor easy understanding of the solvation process and separation of effects of different nature, it is convinient in the continuum theory to split the solvation process in three imaginary steps: 1) creation of the cavity , 2) turning on dispersion-repulsion forces and, then 3) electrostatic forces. Dispersion-repulsion forces and cavitation contribution to the energy normally comes with opposite signs, therefore, reducing the total contribution. In many cases, specifically for the case of charged or highly polar solutes, electrostatic forces play the dominant role. Additionally, during the chemical reaction, cavitation and repulsion forces do not change much, and therefore, if we are concerned with the effect of solvent on reaction, they may be neglected.
7 Basics of the Continuum Model Theory Solvent is described in terms of macroscopic propertiesSolvent is dielectric medium (uniform, normally), characterized by the dielectric constant e0Polarization of solvent is expressed in terms of the surface charge density on the cavity surfacePolarization produces the electric field in the cavity making an effect on soluteDispersion-Repulsion and Cavitation are added separately, or ignoredAs I just told, solvent in the continuum model described in terms of the macroscopic properties. To count electrostatic effect, solvent is described as dielectric medium characterized in most cases, by a single property, which its dielectric constant. As it can be derived from the electrostatic, the polarization of solvent can be expressed in terms of the surface charge density on the cavity surface. Having the surface charge calculated we can calculate the electric field in the cavity and its effect on solute. If the surface charge on the cavity surface is calculated. Cavitation and Dispersion-Repulsion contribution does not affect the QM part of calculation and are calculated separately afterwards, or ignored. Both these contributions calculated using the atomic accessible surface areas (ASAs) and basic formulas derived from a general theory of liquids
8 The electrostatic problem Poisson equationswith boundary conditionson S:Solution is calculated as
9 Born Model A single charge inside a spherical cavity No constructing of the cavity surface elements, because the Poisson equation is solved analytically
10 Onsager Model Spherical cavity Dipolar reaction field No constructing of the cavity surface elements, because the Poisson equation is solved analyticallyKeywords in Gaussian:SCRF(Dipole,A0=value,Dielectric=value)Area of applicability:Solute shape is close to sphericalSolute is polar (m >> 0)ReferencesL. Onsager, J. Am. Chem. Soc. 58, 1486 (1936).M. Wong, M. Frisch, K. Wiberg, J. Am. Chem. Soc. 113, 4476 (1991).
11 Polarized Continuum Model (PCM) Realistic molecular shape of the cavity (interlocking spheres around each atom or group, or isodensity surface)Induced surface charges represent solvent polarizationIncludes free energy contributions from forming the cavity and dispersion-repulsionComes in number of “flavours”: IEFPCM, CPCM, DPCM, IPCM, or SCIPCMKeywords in Gaussian:SCRF(Solvent=, PCM specific options)References:E. Canses, B. Mennucci, J. Tomasi, J. Chem Phys. 107, 3032 (1997).J. Tomasi, M. Persico, Chem. Rev. 94,2027 (1994).J. Tomasi, B. Mennucci, R. Camm, Chem. Rev. 105, 2999 (2005).
12 PCM, the cavity construction Interlocking spheres around atomic groupsThis is default in Gaussian 03A choice of united atoms radii set, RADII=UAO (default), UAHF, UAKS, or UFFInterlocking spheres around each atomRadii=Pauling (or Bondi)Requires the scaling factor ALPHA by which the sphere radius is multiplied. The default value is 1.0 though should be 1.2A number of keywords is provided to add extraspheres when necessaryA number of keyword is provided to govern the size and number of surface elements (tesserae)UA0: Use the United Atom Topological Model applied on atomic radii of the UFF force field.UAHF: Use the United Atom Topological Model applied on radii optimized for the HF/6-31G(d) level of theory. These are the recommended radii for for the calculation of ΔGsolvation via the SCFVAC PCM keyword.UAKS: Use the United Atom Topological Model applied on radii optimized for the PBE0/6-31G(d) level of theory.UFF: Use radii from the UFF force field. Hydrogens have individual spheres (explicit hydrogens).PAULING: Use the Pauling (actually Merz-Kollman) atomic radii (explicit hydrogens).BONDI: Use the Bondi's atomic radii (explicit hydrogens).
13 PCM, the cavity view Keyword: GeomView Creates files in GeomView format to visualize the cavity construction and the charge distribution on the cavity:tesserae.offcharge.offFiles are readable by GeomView, JavaView and other visualization software.(C5NH12+)It is useful to check the surface created by Gaussian before going in furhter calculations.
14 PCM, methods of solving of the SCRF problem to calculate surface charges IterativeKeyword: ITERATIVESolves the PCM electrostatic problem through a linear scaling iterative method using a Jacobi-like schemeAdvantageous when memory is limited.InversionKeyword: INVERSIONSolve the PCM electrostatic problem to calculate polarization charges through the inversion matrix D with dimension of NtesxNtesGaussian 03 uses Inversion by default.
15 Dielectric PCM The original version of PCM Electrostatics directly from the cavity modelCharges produces by discontinuity in the electric field across the boundary created by the cavityVery sensitive to solute charge outside the cavityOnly single point calculationsNo longer recommended
16 Integral Equation Formalism PCM (IEFPCM) Default in Gaussian 03Less sensitive to diffuse solute charge distributionsPCM + careful outlying charge corrections => IEFPCM
17 CPCM (Cosmo)Uses the assumption that the cavity surface to be conductor-likeThis assumption simplifies the solution of Poisson equation and calculation of the surface chargesResults can be outputted in COSMO RS formatNot recommended for solvents with low polarityIt is more efficient in iterative regimeCOSMO RS (COSMO Realistic Solvation) calculate the thermodynamic data from molecular surface polarity distributions resulting from COSMO calculations of the individual compounds in the mixture.
18 Isodensity PCM (IPCM) and Self-Consistent Isodensity PCM (SCIPCM) Cavity formed using gas-phase static electronic isodensity surface (IPCM)Less arbitrary than spheres on atomsCavity changes with electron density and environmentThe default density value isonly single point calculationsSelf-Consistent Isodensity (SCIPCM)iterations are folded in SCFissues regarding scaling of charges still remainReferencesJ. Foresman, T.Keith, K. Wiberg, J. Snoonian, M. Frisch, J. Phys. Chem. 100,16098 (1996).
19 Gaussian 03 Keyword Examples SCRF(Dipole,A0=5.5,eps=78.39)SCRF(IEFPCM) is the same as SCRF(PCM), or just SCRFSCRF(CPCM,Solvent=THF,Read)SCRF(IPCM)SCRF(SCIPCM)Emphasise read thing
20 Sample input for PCM calculations PCM solvation is requested. Solvent is Water. Additional PCM specific keywords are provided%chk=pip-pcm#P HF/6-31g(d) SCRF(PCM,Solvent=Water,Read) testPiperidinium cation1 1NCCCCCHHHHHHHHHHHHPCMDOCITERATIVEGEOMVIEW25 solvent are hardwired. Alternatively, the dielctric constant eps and solvent radius can be set up manually.PCM specific keywords
21 Sample output SCF Done: E(RHF) = -250.669391936 A.U. after 6 cycles Convg = D V/T =S**2 =Variational PCM results=======================<psi(f)| H |psi(f)> (a.u.) =<psi(f)|H+V(f)/2|psi(f)> (a.u.) =Total free energy in solution:with all non electrostatic terms (a.u.) =(Polarized solute)-Solvent (kcal/mol) =Cavitation energy (kcal/mol) =Dispersion energy (kcal/mol) =Repulsion energy (kcal/mol) =Total non electrostatic (kcal/mol) =
23 Piperedin cation (C5NH12+), free energy of hydration QM: HF/6-31G(d)MethodDGsolv, kcal/molSP SCRF(Dipole,A0=5.5)-30.6SP SCRF(PCM)-56.0SP SCRF(CPCM)-56.1SP SCRF(IPCM)-59.4SP SCRF(SCIPCM)-60.9Opt SCRF(PCM)-56.3Opt SCRF(CPCM)-56.4Opt SCRF(SCIPCM)-61.1Experiment-60.0SP timing: sec., Opt 2-3 min. using Itanium2 CPUNon-electrostatic: +4.3 kcal/molPCM cavity was constructed of 1006 tesseraeDipole, IPCM and SCIPCM results includes electrostatic effects only, sum of non-electrostatic is kcal/mol (PCM).
24 ET system Donor = 4-Biphenyl Acceptor = 2-Naphthyl e- D-SA → DSA- Spacer: 5-a-androstaneFirst, DSA structure in its neutral state (to avoid biasing) was optimized in vacuo.
25 Method to solve surface charges ET systemD-SA → DSA-D: 4-BiphenylA: 2-NaphthylS:5-a-androstane87 atoms in total,5158 tesserae createdET systemROHF/6-31G(d,p) SP SCRF(IEFPCM, Solvent=THF)Method to solve surface chargesMemory,MbCPUsTime, min.Matrix inversion(default)240192.56403280031160030422Iterative6428292740017.5
26 Method to solve surface charges ET systemD-SA → DSA-D: 4-BiphenylA: 2-NaphthylS:5-a-androstane87 atoms in total,5158 tesserae createdROHF/6-31G(d,p) SP SCRF(СPCM, Solvent=THF)Method to solve surface chargesMemory,MbCPUsTime, min.Matrix inversion(default)240129640800281600419Iterative64165.75
27 ET systemIn vacuo ROHF and UHF calculations fails to produce the precursor state. Altering of MOs does not help.Polarization field of solvent makes it possible to obtain solution (with solvent polarization effects included!) for both precursor and successor statesDG = -7.7 kcal/mol (IEFPCM)DG = -9.6 kcal/mol (СPCM)DG = -2.7 kcal/mol (СPCM, optimization, 78 hrs.)DG = -5±1 kcal/mol (Experiment)using guess=alter option and altering order of HOMO and LUMOET molecules without cavity.Blue structure is the precursor, 4-biphenyl is planarRed structure is successor, 4-biphenyl dihedral angle is 42.9º
28 Menshutkin reaction What is DG and DG≠ for the reaction? NH3 CH3Cl NH3CH3+ Cl-What is DG and DG≠ for the reaction?What is the nature of the transition state?How does solvent change the result?Methylation of tetriary amines to quaternary ammonium salt by reaction with an alkyl halide
29 Menshutkin reaction DG≠ DG Model Gas 43.7 120.0 Onsager 18.2 10.0 NH3 CH3Cl NH3CH3+ Cl-ModelDG≠DGGas43.7120.0Onsager18.210.024.2-21.0CPCM24.8-21.5Experiment – for CH3I?110Solution24-30Energies in kcal/molMethylation of tetriary amines to quaternary ammonium salt by reaction with an alkyl halide
30 Menshutkin reaction: Transition State ModelC-NC-ClH-N-CCl-C-HGas1.7652.571110.678.7Onsager2.2732.250112.694.2CPCM2.1452.249110.392.6
31 RecommendationsPreliminary in vacuo calculations (geometry and wavefunction guess)In many cases SP SCRF after Optimization in vacuo is enoughIEFPCM ( It is the default method in G03)When memory is limited, or the system is large, the Iterative algorithm is faster and less demanding than InversionWhen time is crucial, CPCM is recommended under some conditions:polar solvent;keyword Iterative!