1. Calculating Molecular Properties
from molecular orbital calculations

2. Geometric Properties Bond length Bond angle Dihedral angle
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) d2E/dBdI
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) Electron affinity (EA)
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 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.*
CH3CH2CH2CH C C
CH3CH=CHCH C C
benzene (C6H6)
* 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
Shift Diff.
HF/6-31G(d)
HF/6-31G(d,p)
HF/6-31++G(d,p)
(observed)

14. IR Frequency Calculations
Formaldehyde
C-H bend C=O stretch
Computed Frequency cm cm-1
Relative intensity
Freq. scaled by cm cm-1
observed cm cm-1

15. IR Frequencies (cm-1, gas phase)
Scaled Frequency Expt.

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) =
Thermal correction to Energy=
Thermal correction to Enthalpy=
Thermal correction to Gibbs Free Energy=
Sum of electronic and zero-point Energies=
Sum of electronic and thermal Energies=
Sum of electronic and thermal Enthalpies=
Sum of electronic and thermal Free Energies=

19. Frequency calculation...
Heat capacity
Entropy
E (Thermal) CV S
Kcal/mol cal/mol-Kelvin cal/mol-Kelvin
TOTAL
ELECTRONIC
TRANSLATIONAL
ROTATIONAL
VIBRATIONAL
Gº = H º - TS º
= * / * 1000
(in Hartrees)
(kcal/mol per Hartree)

20. Dipole Moment (in Debyes) HF / HF / MP2 /
MMFF AM1 PM G* G** “ Expt. NH
H2O
P(CH3)
thiophene
(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 MMFF AM1 PM G* G** “ Expt.
acetone
(trans/gauche)
N-Me formamide
(trans/cis)
1,2-diF ethane
(gauche/anti)
1,2-diCl ethane
(anti/gauche)

22. Equilibrium Bond Length
(in Å)
HF / HF / MP2 /
Sybyl MMFF AM1 PM G* G** “ Expt.
propane
(C-C single)
propene
(C=C double)
1,3-butadiene
(C=C double)
propyne
(CC triple)

23. Log P Log P = Log K (o/w) = Log [X]octanol/[X]water
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).