Calculating Molecular Properties

1. Calculating Molecular Properties from molecular orbital calculations

2. Geometric Properties A single lowest energy equilibrium structure is generally the result of a geometry optimization; actual molecules exist as an ensemble (mixture) of conformations which is temperature dependent. • Bond length • Bond angle • Dihedral angle Experimental measurements of geometry (X-ray, ED, NMR, ND) measure different aspects of structure.

3. Molecular Properties • Many are first, second or third derivatives of the Hartree-Fock energy (E) with respect one or more of the following: • external electric field (F) • nuclear magnetic moment (nuclear spin, I) • external magnetic field (B) • change in geometry (R)

4. Examples…derivatives w/r to: • external electric field (F): • Raman intensity d3E/dRdF2 • nuclear magnetic moment (nuclear spin, I) • ESR hyperfine splitting (g) dE/dI • NMR coupling constant (Jab) d2E/dIadIb

5. Examples... • external magnetic field (B) and (nuclear spin, I) • NMR shielding (s) d2E/dBdI • Change in geometry (R) • Energy Gradient dE/dR • Hessian (force constant; IR vibrational frequencies) d2E/dR2

6. Other Properties • Ionization energy (IP) • Neg. of HOMO energy (Koopmans’ theorem) Errors due to relaxation and electron correlation CANCEL • Electron affinity (EA) • LUMO energy Errors due to relaxation and electron correlation ADD • UV-Vis spectra • Est. (poorly) by HOMO-LUMO energy difference

7. UV-Vis Spectra • Can be estimated as the HOMO-LUMO energy difference • Generally not very accurate because orbital relaxation and electron correlation effects are ignored, but useful for relative wavelengths, and to predict trends • Difficult to model effects of solvent, especially on excited states, about which little is known. • Density functional theory (to be discussed later) generally does a better job at predicting UV-Vis spectra.

8. Problems with UV-Vis spectra • The energy required to promote an electron from MO i to MO j is not simply equal to the energy difference e(j) - e(i). The promotion energy E(i-->j) can be expressed as: E(i-->j) = e(j) - e(i) - v(i,j) • The wavefunction |i-->j| of an excited electronic configuration is not a good approximation to an eigenfunction of the many-electronic Hamilton operator H. Excited configurations tend to interact, and a proper description must include Configuration Interaction (CI) to account for electron correlation.

9. Other Properties... • IR spectra (bond vibrational frequencies) • frequencies are over-estimated by H-F theory; a scaling factor of 0.89-0.91 must be applied to reproduce observed values • Proton affinity (related to basicity, but is calculated in the gas phase rather than in aqueous solution)

10. Other Properties... • Acidity • Gibbs Free energy (G) • Includes Enthalpy (H) and Entropy (S) • A frequency calculation must be performed on an energy minimized structure to obtain thermal corrections, which allow calculation of entropy and other values. (later)

11. Other Properties... • Charges on Atoms in Molecules • meaning of charge is ill-defined • value depends on definition • several commonly used charge estimations • Mulliken • Natural population analysis • Charges fit to electrostatic potential • Atoms in molecules (AIM) • ChelpG (topic of a later lecture)

12. NMR chemical shift calculations (in ppm) calc. expt.* CH3CH2CH2CH3 C1 15.9 13.4 C2 23.7 25.2 CH3CH=CHCH3 C1 18.4 17.6 C2 124.7 126.0 benzene (C6H6) 128.9 130.9 * in CDCl3 solution

13. NMR: Effect of Basis Set Calculated chemical shifts (ppm) and difference from gas phase experimental values as a function of basis set ShiftDiff. HF/6-31G(d) 127.3 -3.6 HF/6-31G(d,p) 128.4 -2.5 HF/6-31++G(d,p) 128.9 -2.0 (observed) 130.9 --

14. IR Frequency Calculations Formaldehyde C-H bendC=O stretch Computed Frequency1336 cm-1 2028 cm-1 Relative intensity 0.4 150.2 Freq. scaled by 0.89 1189 cm-1 1805 cm-1 observed 1180 cm-1 1746 cm-1

15. IR Frequencies (cm-1, gas phase) Scaled FrequencyExpt. 18051746 17991737 18501822 17971761

16. Zero-point energy Energy possessed by molecules because v0, the lowest occupied vibrational state, is above the electronic energy level of the equilibrium structure. Usual calc’c energy

17. Thermal Energy Corrections • The following may be derived from the results of a frequency calculation: • Zero Point Energy (z.p.e.) • Free Energy at STP (Gº) • Free Energy at another Temperature, Pressure • Entropy (S) • Enthalpy (H) corrected for thermal contributions • Constant-volume heat capacity (Cv)

18. Frequency calculation • Formaldehyde was optimized and a frequency calculation performed in Gaussian 98 at NCSC. Zero-point correction (all in Hartrees/Particle) = 0.028987 Thermal correction to Energy= 0.031841 Thermal correction to Enthalpy= 0.032785 Thermal correction to Gibbs Free Energy= 0.007373 Sum of electronic and zero-point Energies= -113.840756 Sum of electronic and thermal Energies= -113.837902 Sum of electronic and thermalEnthalpies= -113.836958 Sum of electronic and thermalFree Energies= -113.862370

19. Frequency calculation... Heat capacity Entropy E (Thermal) CV S Kcal/molcal/mol-Kelvincal/mol-Kelvin TOTAL 19.980 6.26053.483 ELECTRONIC 0.000 0.000 0.000 TRANSLATIONAL 0.889 2.981 36.130 ROTATIONAL 0.889 2.981 17.303 VIBRATIONAL 18.203 0.298 0.050 Gº = H º - TS º -113.862370 = -113.836958- 298.15 * 53.483 / 627.5095 * 1000 (in Hartrees) (kcal/mol per Hartree)

20. Dipole Moment (in Debyes) HF / HF / MP2 / MMFFAM1PM33-21G*6-311+G** “ Expt. NH3 2.04 1.85 1.55 1.75 1.68 1.65 1.47 H2O 2.46 1.86 1.74 2.39 2.12 2.08 1.85 P(CH3)3 2.06 1.52 1.08 1.28 1.44 1.31 1.19 thiophene 1.32 0.34 0.67 0.76 0.80 0.47 0.55 (note that none are very accurate; this reflects two factors: equilibrium geometry is only one of several, even many, in an ensemble of conformations, and charges are ill-defined.

21. Conformational Energy Difference (in kcal/mol) Good: Generally poor: HF / HF / MP2 / Sybyl MMFFAM1PM33-21G*6-311+G** “ Expt. acetone (trans/gauche) 0.6 0.8 0.7 0.5 0.8 1.0 0.6 0.8 N-Me formamide (trans/cis) -1.8 2.6 0.4 -0.5 3.9 2.7 2.7 2.5 1,2-diF ethane (gauche/anti) 0.0 -0.6 -0.5 1.4 -0.9 0.3 0.8 0.8 1,2-diCl ethane (anti/gauche) 0.0 1.2 0.8 0.6 1.9 1.9 1.3 1.2

22. Equilibrium Bond Length (in Å) HF / HF / MP2 / Sybyl MMFFAM1PM33-21G*6-311+G** “ Expt. propane (C-C single) 1.551 1.520 1.501 1.512 1.541 1.525 1.526 1.526 propene (C=C double) 1.334 1.334 1.331 1.328 1.316 1.316 1.336 1.318 1,3-butadiene (C=C double) 1.338 1.338 1.335 1.331 1.320 1.320 1.342 1.345 propyne (CC triple) 1.204 1.201 1.197 1.192 1.188 1.181 1.214 1.206

23. Log P Log of the octanol/water partition coefficient; considered a measure of the bioavailability of a substance Log P = Log K (o/w) = Log [X]octanol/[X]water • most programs a use group additivity approach (discussed later, with QSAR) • some use more complicated algorithms, including the dipole moment, molecular size and shape • subject to same limitations as dipole moment

24. Conclusions • Many useful molecular properties can be calculated with reasonably good accuracy, especially if methods including electron correlation and large basis sets are used. • Some properties (charges on atoms, dipole moments, UV-Vis spectra) are not well modeled, even by high level calculations. • Some of the errors are because of problems defining the property (e.g., charge); others are because of limitations of the method (orbital relaxation and electron correlation).