calculating molecular properties from molecular orbital calculations
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Calculating Molecular Properties
from molecular orbital calculations
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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.
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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)
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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
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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
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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
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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.
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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.
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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
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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
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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)
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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
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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 --
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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
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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
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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
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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)
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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
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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
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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.
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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:
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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)
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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
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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).