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Calculation of Molecular Properties: How, What and Why?

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## Calculation of Molecular Properties: How, What and Why?

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**Calculation of Molecular Properties:**How, What and Why? Dr. Vasile Chiş Biomedical Physics Department, Faculty of Physics Babeş-Bolyai University, Cluj-Napoca "Many experimental chemists use various kinds of spectroscopy in their research even though they are not spectroscopists. In a similar manner, more and more scientists are applying computational techniques as another weapon in their arsenal" Delano P. Chong in Recent Advances in Density Functional Methods, Part I, World Scientific, 1995 Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Outline**1. Introduction 2. Hartree-Fock-Roothaan-Hall Theory 3. Basis Sets 4. Electron Correlation 5. ABC of DFT 6. Predictible Molecular Properties 7. Examples of Calculations vibrational, NMR and ESR spectra conformers, tautomers, relative energies, molecular orbitals Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Calculation of Molecular Properties: Why?**Molecular Structures Molecular Properties Spectroscopic Observables Ab Initio Electronic Structure Theory Hartree-Fock DFT Prodding and Helping the Experimentalists Benchmarks for parametrizations Transition States Reaction Coordinates Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**A short history**“We are perhaps not far removed from the time when we shallbe able to submit the bulk of chemical phenomena to calculation” Joseph Louis Gay-Lussac, Memoires de la Societe d’Arcueil, 2,207(1808) J.L. Gay-Lussac “The more progress physical science make, the more they enter the domain of mathematics, which is a kind of centre to which they all converge. We may even judge the degree of perfection to which a science has arrived by the facility with which it may be submitted to calculation.” Adolphe Quetelet, Instructions Populaires sur le Calcul des Probabilities, Tarlier, Brussels, 1828, p. 230 A. Quetelet “Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry. If mathematical analysis should ever hold a proeminent place in chemistry – an aberration which is almost impossible – it would occasion a rapid widespread degeneration of that science” A. Compte, Philosophie Positive, 1830 A. Compte Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Quantum Wave Mechanics, 1926**H=E E.R.J.A. Schrödinger W.K. Heisenberg “The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.” P.A.M. Dirac, Proc. Roy. Soc(London) 123, 714(1929) P.A.M. Dirac Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai**University, Cluj-Napoca**Hartree-Fock-Roothaan Theory**M. Born R. Oppenheimer Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**D. Hartree**Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**D. Hartree**V. Fock Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**D. Hartree**V. Fock C. Roothaan Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Basis Sets**=LCBF {μ} – a set of known functions Slater Type Orbitals (STO) Gaussian Type Orbitals (GTO) Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**allow a more rapidly and efficiently calculation of the**two-electron integrals GTO have different functional behavior with respect to known functional behavior of AOs. S. F. Boys, Proc. Roy. Soc. (London) A200 (1950) 542. Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**6-31G Basis set for CH4 molecule**Standard basis: 6-31G (6D, 7F) Basis set in the form of general basis input: 1 0 S 6 1.00 .3047524880D+04 .1834737130D-02 .4573695180D+03 .1403732280D-01 .1039486850D+03 .6884262220D-01 .2921015530D+02 .2321844430D+00 .9286662960D+01 .4679413480D+00 .3163926960D+01 .3623119850D+00 SP 3 1.00 .7868272350D+01 -.1193324200D+00 .6899906660D-01 .1881288540D+01 -.1608541520D+00 .3164239610D+00 .5442492580D+00 .1143456440D+01 .7443082910D+00 SP 1 1.00 .1687144782D+00 .1000000000D+01 .1000000000D+01 **** 2 0 S 3 1.00 .1873113696D+02 .3349460434D-01 .2825394365D+01 .2347269535D+00 .6401216923D+00 .8137573262D+00 S 1 1.00 .1612777588D+00 .1000000000D+01 **** ... STO-3G 3-21G 6-31G(d) 6-311++G(2df,p) … HF limit: mono-determinantal wave-function + infinite basis set Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Electron Correlation**HF method: electron-electron interaction is replaced by an average interaction E0 – exact ground state energy EHF – HF energy for a given basis set - represents a measure for the error introduced by the HF approximation Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Types of electronic correlation**Spin correlation - effect of the Pauli exclusion principle (Fermi correlation) (Fermi hole) Exchange Energy Dynamical correlation – related to the movements of the individual electrons (Coulomb correlation)(Coulomb hole) Non-dynamical correlation - related to the fact that in certain circumstances the ground state SD wave-function is not a good approximation to the true ground state because there are other Slater determinants with comparable energies (near degeneracy problem) Correlation Energy Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Correlation Energy: Is it important?**N2 molecule: CE ~ 0.5% of the EE ~ 50% of the binding energy! Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**How to take it into account?**multideterminantal wave-function ESD – obtained by replacing MOs which are occupied in the HF determinant by unoccupied MOs - singly, doubly, triply, quadruply, etc. excited relative to the HF determinant Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Electron correlated methods:**Configuration Interaction (CIS, CID, CISD, CISDT, etc.) Multi-Configuration Self-Consistent Field Method (MCSCF) n,m-CASSCF Moller-Pleset Theory MP2, MP4, etc. Coupled Cluster Theory CCD, CCSD, etc. Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**ABC of DFT**1927 L.H. Thomas, E. Fermi 1964 P. Hohenberg, W. Kohn, L.J. Sham 1992 Gaussian® Why a new theory? HF method scales as K4 (K - # of basis functions) CI methods scale as K6-K10 MPn methods scale as >K5 CC methods scale as >K6 Correlated methods are not feasible for medium and large sized molecules! The electron density Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**DFT is presently the most successful and also the most**promising approach to compute the electronic structure of matter. Applicability: atoms, molecules, solids DFT is less computationally expensive than traditional Hartree-Fock methods but it gives similar accuracy. Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**First HK Theorem:**P. Hohenberg W. Kohn Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Modern DFT**FHK ??? Only J[ρ] is known! The explicit form of T[ρ] and Enon-cl[ρ] is the major challenge of DFT Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**T[ρ] – kinetic energy of a real interacting electron**system with density ρ(r) TKS – kinetic energy of a fictitious non-interacting system of the same density ρ(r) Ψi - are the orbitals for the non-interacting system (KS orbitals) T=TKS+(T-TKS) • Exc[ρ] includes everything which is unknown: • exchange energy • correlation energy • correction of kinetic energy (T-TKS) Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Variational Principle in DFT**Second HK Theorem Minimize E[ρ] with the conditions: Kohn-Sham Equations: W. Kohn L.J. Sham with: Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Kohn-Sham Formalism**W. Kohn L.J. Sham Kohn-Sham equations Hartree-Fock equations Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Exc[ρ] = ??**Local Density Approximation (LDA) εxconly depends on the density at r Generalized Gradient Approximation (GGA) εxc depends on the density and its gradient at r Hybrid Functionals Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**DFT: a new and powerful tool in chemical physics**Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Predictible Molecular Properties**Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Examples of Calculations**• pyrazinamide • meta-benzosemiquinone anion free radical • 5-pBBTT Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**analogue of nicotinamide**• very important drug used to treat tuberculosis • some transition metal(II) molecular complexes of this molecule are recognized and used as antimycobacterial agents • Pyrazinamide (PZA) Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**C2**C1 Optimized geometries (B3LYP/6-31G(d)) of the two conformers of PZA Possible contributions from both conformers (in gas or liquid phase) Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Interaction energy:**Basis set superposition error Optimized geometry (B3LYP/6-31G(d)) of the PZA dimer ΔEuncorrected = 16.14 Kcal/mol ΔECPcorrected = 13.82 Kcal/mol HB – moderate strength - predominant electrostatic character G.A. Jeffrey, An Introduction to Hydrogen Bonding, Oxford University Press, New York, 1997 Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Selected experimental and calculated vibrational bands of**PZA NH2 – important role in the conformation of peptides or Watson-Crick complexes - intermediates the hydrogen bonds (intra and inter) Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Experimental and calculated NMR spectrum of PZA**HB Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**[1H, 1H] COSY45 NMR spectrum of pyrazinamide in DMSO**solution Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**For a reliable assignment of experimental spectra**- intermolecular interactions must be considered! - minimal computational strategy: vibrational spectra DFT (B3LYP + BLYP) monomer + dimer calculations 6-31G(d) basis set NMR spectra DFT (B3LYP) dimer calculations cc-pVDZ basis set Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**ortho**meta para ESR spectra of ortho-, meta- and para-benzosemiquinone radicals Quinones (and related radicals) are involved in many biophysical processes: • cellular respiration (ubiquinone = coenzyme Q10) - also, an essential nutrient • blood clotting (menaquinones = vitamin K2) • aging (tocoquinones = vitamin E2) • microbial controlling agents quinone-type radicalsimportant cofactors for electron transfer in photosynthesis very accessible to experimental and theoretical analyses Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**BSQ anion radicals: energetics, structures and symmetries**B3LYP/6-31+G(d) Cs symmetry 7.38Kcal/mol 7.15Kcal/mol Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**BSQ anion radicals: HOMO and LUMO’s energies**B3LYP/6-31+G(d) Cs symmetry Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**BSQ anion radicals: HOMOs, LUMOs, USDs**HOMO LUMO USD Distribution ortho meta para Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**meta-BSQ optimized structures**B3LYP/EPR-II Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Calculated hyperfine coupling constants of the**meta-BSQ anion radical in gas-phase, for the three minimum structures * absolute values Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Gas-phase meta-benzosemiquinone anion radical**+ - + B3LYP/EPR-II (grid ultrafine) 0.27 -11.76 2.87 Marked non uniformity of the electron density in C1C2C3 region Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Experimental and calculated wave-numbers for m-BSQ anion**radical G.N.R.Tripathi, D.M.Chipman, C.A.Miderski, H.F.Davis, R.W.Fessenden, R.H. Schuler, J.Phys.Chem., 90,3968(1986) present work CH bend CO stretch *B3LYP/6-31+G(d) Cs symmetry Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Conclusions**• dipole moments: (ortho)> (meta)>(para)=0 • number of minimum energy conformers: 2 for ortho and para, 3 for meta • total energies: Emeta>Eortho>Epara • hfcc’s: ortho - strong influence of the solvation effects meta - marked non-uniformity in the electron density para – easilly reproduced even in gas-phase • vibrational spectra: ortho – no experimental data available meta – reassignment of two bands in the IR spectrum para – very good agreement between experiment and theory Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Vibrational, NMR and DFT investigation of 5-pBBTT**Molecular structure and atom numbering scheme for 5-para-bromo-benzilidene- thiazolidine-2-thion-4-one molecule Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**5-pBBTT Conformers and Tautomers**C1 C2 C2 Thiol C1 Thiol C1 Thiol 1 C2 Thiol 1 Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**X-ray diffraction**Unit cell parameters a = 4.4597(7) Å b = 12.5508(19) Å c = 13.727(2)Å α = 90.751(2) β = 96.230(2) γ = 97.865(3) Crystal System: Triclinic Space group: P-1 Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**1H NMR Spectrum of 5-pBBTT in DMSO**Looking for a proton Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca**Different tautomers in liquid state?**Experimental: 3.4ppmand13.9 ppm Thione Conformer Thiolic Conformer Calculated chemical shift for N-H and S-H protons in thione and thiol tautomers Thiol: 66% Thione: 33% Dr. Vasile Chiş, Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca