《分子电子结构》研究生课程教学资源（Electronic Structure of Molecules）9-solvation

Lasttime1. Geometry optimization2. Vibrational normal mode3. Frequency calculation4. IR and Raman5. Thermochemistry2

Last time 2 1. Geometry optimization 2. Vibrational normal mode 3. Frequency calculation 4. IR and Raman 5. Thermochemistry

Contents1. Explicit solvation models2. Implicit solvation modelsForesmanandFrisch,Chapter5Jensen,Chapter15.63

Contents 3 1. Explicit solvation models 2. Implicit solvation models Foresman and Frisch, Chapter 5 Jensen, Chapter 15.6

Fromvacuumto liquidOur calculations are all in vacuum;- Thermochemistry is based on the gas phase model, i.e., theideal gas model;Vacuum or gas phase properties can be extended to condensedphase?- Geometry, charge, dipole, spectra, bonding, and reactivity?The key change is the solvation free energy;- The net energy change upon transferring the molecule fromthe gas phase into a solvent with which it equilibrates;△Gsol = Gsol -Ggas4

From vacuum to liquid • Our calculations are all in vacuum; – Thermochemistry is based on the gas phase model, i.e., the ideal gas model; • Vacuum or gas phase properties can be extended to condensed￾phase? – Geometry, charge, dipole, spectra, bonding, and reactivity? • The key change is the solvation free energy; – The net energy change upon transferring the molecule from the gas phase into a solvent with which it equilibrates; 4 ΔGsol = Gsol – Ggas

Freeenergysurfacefromgasto liquidgas-phaseThick lines on the two surfacessurfaceindicate some chemicalreaction proceeding fromoneAGg(x,y)minimum-energy structuretoanother;EsolvatedNote that there is nosurfacerequirement forthe x and ycoordinates of equivalentstationary points on the two[ (x,y)surfaces to be the same;△Gsol = Gsol - GgasPolarsolvents shift theequilibrium to right;5

Free energy surface from gas to liquid • Thick lines on the two surfaces indicate some chemical reaction proceeding from one minimum-energy structure to another; • Note that there is no requirement for the x and y coordinates of equivalent stationary points on the two surfaces to be the same; 5 ΔGsol = Gsol – Ggas • Polar solvents shift the equilibrium to right;

Born-HabercycleforcomputationofafreeenergychangeinsolutionAG (gas)BW(gas) +A(gasX(gas) +(gas)AGS(W)AG%(A)△G%(B)AG(X)e.g.Menschutkin△G%(...)AG%(.)reaction has differentB(sol)W(sol)energy profiles in gasA(sol)X(sol)+4AG(snhandinwaterAGgasGs(+)HoNgasTAGgasphaseaqueousAGs(R)AGs(FsolutionGStHaNCH + CINHa + CHgCIAGSolR*QReaction coordinate6Arbitrary coordinate

Born–Haber cycle for computation of a free￾energy change in solution 6 e.g. Menschutkin reaction has different energy profiles in gas and in water

ExplicitsolventmodelsIncludes individual solvent molecules;If solution is dilute, how to construct its solvation shell?-How many shells? Geometry of solvent molecules?How todeal withthe boundary?- Require 100-1000 of solvent molecules surrounding thesolute;Calculatethefreeenergyof solvationbysimulating solutesolvent interactions;Verylengthycalculations;Requires an empirical interaction potential between thesolvent and solute, and between the solvent molecules;

Explicit solvent models • Includes individual solvent molecules; • If solution is dilute, how to construct its solvation shell? – How many shells? Geometry of solvent molecules? How to deal with the boundary? – Require 100-1000 of solvent molecules surrounding the solute; • Calculate the free energy of solvation by simulating solute￾solvent interactions; • Very lengthy calculations; • Requires an empirical interaction potential between the solvent and solute, and between the solvent molecules; 7

QM/MMQuantum mechanical treatment of the solute andmolecular mechanical treatment of the solvent;-Replacesthesolventmoleculeswithpartialcharges;- e. g., TIP3P uses S+ = 0.417 and S- = -0.834;S+H-O18+HRestricted to research groups that specialize in suchthings;: GAMESS-US (effective fragment potential, EFP);Good“blackbox"implementationsare notgenerallyavailable;8

QM/MM • Quantum mechanical treatment of the solute and molecular mechanical treatment of the solvent; – Replaces the solvent molecules with partial charges; – e. g., TIP3P uses δ+ = 0.417 and δ– = –0.834; 8 • Restricted to research groups that specialize in such things; • GAMESS-US (effective fragment potential, EFP); • Good “black box” implementations are not generally available;

MonteCarlosimulationsBox containing a solute and solvent molecules(periodic boundary conditions); Random moves of molecules;If energy goes down, accept the move;If energy goes up, accept according to Boltzmannprobability; MC calculations can be used to compute free energydifferences, radial distribution functions, etc.; Cannot be used to compute time dependentproperties such as diffusion coefficients, viscosity,etc.9

Monte Carlo simulations • Box containing a solute and solvent molecules (periodic boundary conditions); • Random moves of molecules; • If energy goes down, accept the move; • If energy goes up, accept according to Boltzmann probability; • MC calculations can be used to compute free energy differences, radial distribution functions, etc.; • Cannot be used to compute time dependent properties such as diffusion coefficients, viscosity, etc. 9

MolecularDynamicssimulations· Use classical equations to simulate themotion of the molecules for a suitablylong time (100's ps to ns);Requires energies and gradients of thepotential; In addition to free energies, can be usedto compute time dependent propertiestransport properties, correlation functions,etc.;10

Molecular Dynamics simulations • Use classical equations to simulate the motion of the molecules for a suitably long time (100’s ps to ns); • Requires energies and gradients of the potential; • In addition to free energies, can be used to compute time dependent properties transport properties, correlation functions, etc.; 10

But,theelectronicstructureischanged!"lt cannot be overemphasized that solvation changesthe solute electronic structure.Dipole moments insolutionare largerthanthecorresponding dipolemoments in the gas phase. Indeed, any property thatdependsontheelectronicstructurewilltendtohaveadifferentexpectationvalueinsolutionthaninthegasphase."Table11.1Nucleic acid base dipolemoments (D)attheSM5.42R/HF/6-31G(d)levelMoleculeDipolemomentGasWaterChloroform2.42.93.1Adenine6.58.08.5Cytosine5.36.77.1Guanine6.47.88.2Hypoxanthine5.64.46.0Thymine4.55.66.0UracilCramer,EssentialsofComputationalChemistry:TheoriesandModels,Chp1111HF/6-31G(d)levelusingtheSM5.42Rcontinuumsolvationmodel

“It cannot be overemphasized that solvation changes the solute electronic structure. Dipole moments in solution are larger than the corresponding dipole moments in the gas phase. Indeed, any property that depends on the electronic structure will tend to have a different expectation value in solution than in the gas phase.” 11 But, the electronic structure is changed! Cramer, Essentials of Computational Chemistry: Theories and Models, Chp 11 HF/6-31G(d) level using the SM5.42R continuum solvation model