Calculating Molecular Properties

from molecular orbital calculations

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.

Experimental measurements of geometry (X-ray, ED, NMR, ND) measure different aspects of structure.

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)

Examples…derivatives w/r to:

external electric field (F): Raman intensity

E/RF2

nuclear magnetic moment (nuclear spin, I) ESR hyperfine splitting (g)

E/I NMR coupling constant (Jab)

E/IaIb

Examples...

external magnetic field (B) and (nuclear spin, I) NMR shielding (

E/BI

Change in geometry (R) Energy Gradient

E/R Hessian (force constant; IR vibrational frequencies)

E/R

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

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.

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.

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)

RNH2 + H RNH3

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)

RCO2H RCO2 + H

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)

NMR chemical shift calculations

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 ppm)

* in CDCl3 solution

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) 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 --

IR Frequency Calculations

Formaldehyde

C-H bend C=O stretch

Computed Frequency 1336 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

C

O

H H

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

1805 1746

1799 1737

1850 1822

1797 1761

C

O

H H

C

O

CH3 CH3

C

O

CH3 Cl

C

O

CH3 OCH3

Zero-point energy

Energy possessed by molecules because v0, the lowest occupied vibrational state, is above the electronic energy level of the equilibrium structure.

v1v2v3

v0

r0, r1, r2...

Energy

Distance between atomseq. bond length

zero point energy

Usual calc’c energy

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)

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 thermal Enthalpies= -113.836958 Sum of electronic and thermal Free Energies= -113.862370

Frequency calculation...

E (Thermal) CV S

Kcal/mol cal/mol-Kelvin cal/mol-Kelvin

TOTAL 19.980 6.260 53.483

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)

Heat capacity Entropy

Dipole Moment HF / HF / MP2 / MMFF AM1 PM3 3-21G* 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

(in Debyes)

(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.

Conformational Energy Difference

HF / HF / MP2 / Sybyl MMFF AM1 PM3 3-21G* 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

(in kcal/mol)Generally poor:

Good:

Equilibrium Bond Length

HF / HF / MP2 / Sybyl MMFF AM1 PM3 3-21G* 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(CC triple) 1.204 1.201 1.197 1.192 1.188 1.181 1.214 1.206

(in Å)

Log PLog 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

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).