Electronic Spectra of Polyatomic Molecules

The performance of 24 density functionals, including 14 meta-generalized gradient approximation (mGGA) functionals, is assessed for the calculation of vertical excitation energies against an experimental benchmark set comprising 14 small- to medium-sized compounds with 101 total excited states. The experimental benchmark set consists of singlet, triplet, valence, and Rydberg excited states. The global-hybrid (GH) version of the Perdew-Burke-Ernzerhoff GGA density functional (PBE0) is found to offer the best overall performance with a mean absolute error (MAE) of 0.28 eV. The GH-mGGA Minnesota 2006 density functional with 54% Hartree-Fock exchange (M06-2X) gives a lower MAE of 0.26 eV, but this functional encounters some convergence problems in the ground state. The local density approximation functional consisting of the Slater exchange and Volk-Wilk-Nusair correlation functional (SVWN) outperformed all non-GH GGAs tested. The best pure density functional performance is obtained with the local version of the Minnesota 2006 mGGA density functional (M06-L) with an MAE of 0.41 eV.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1574&context=chem_pubs

Benchmarking the Performance of Time-Dependent Density Functional Methods

Self-consistent-field ab initio calculations of the equilibrium geometries, r calc e, and quadratic force constants for methane, ethane, propane, ethene, cyclopropane and cyclopropene have been carried out using an extended basis of contracted gaussian functions (4–31G). In the case of unstrained saturated molecules or parts of molecules a simple (anharmonicity) correction yields calculated structures for which the average deviation with ‘best’ experimental bond lengths and angles is 0·003 A and 0·4° respectively. Calculated carbon-carbon double bonds are typically too short by a constant amount (0·022 A). The average deviation of calculated and experimental bond angles about CH2 groups in three membered rings and those about sp2 hybridized carbons are 1·5° and 1·0° respectively. Quadratic force constants for symmetric stretchings are compared with force constants deduced from vibrational analysis. Trends and differences are discussed.

Application of self-consistent-field ab initio calculations to organic molecules

The complete GVFF of ethane, propane and cyclopropane has been calculated from ab initio energies using an extended (4–31G) basis set. A scale factor method was developed to scale down the ab initi...

Application of self-consistent-field ab initio calculations to organic molecules: II. Scale factor method for the calculation of vibrational frequencies from ab initio force constants: ethane, propane and cyclopropane

https://iopscience.iop.org/article/10.1088/0034-4885/8/1/312/pdf

Molecular electronic spectra, dispersion and polarization: The theoretical interpretation and computation of oscillator strengths and intensities

An interpretation of the long wave‐length absorption regions of conjugated aldehydes and ketones is given. The strong regions can be assigned to transitions of the N→V1 type known to produce the intense long wave‐length absorption in polyenes. The weak absorption regions, which are characteristic of the carbonyl group, can be explained as arising from the type of transition previously proposed to explain the weak carbonyl absorption in saturated aldehydes and ketones. This transition involves the excitation of a loosely bound electron occupying a nonbonding orbital lying in the molecular plane and across the C–O direction, to an excited molecular orbital with a node in this plane. In conjugated molecules several of these excited MO's exist and transitions to them all are predicted. The longest wave‐length carbonyl absorption represents a transition to the lowest of these MO's and the observed shift of this absorption toward longer wave‐lengths with each addition to the number of conjugated bonds in the ch...

The Long Wave‐Length Spectra of Aldehydes and Ketones Part II. Conjugated Aldehydes and Ketones

The A2 and B2 torsional vibrational frequencies in propane gas have been directly measured at 217 ± 8 and 265 ± 8 cm−1, respectively, with inelastically scattered neutrons using the “small κ” method of neutron molecular spectroscopy. The theoretical basis of the scattering experiment is discussed, and factors affecting resolution and intensity are enumerated. Not subject to the same selection rules as optical spectroscopy, neutron molecular spectroscopy is capable of observing vibrational transitions which are otherwise forbidden by molecular symmetry. The vibrational frequencies are interpreted by numerically solving the two‐dimensional wave equation giving librational motion with a two‐dimensional Fourier expansion. In this approach, the potential energy is conveniently expanded also in Fourier form and we obtain a V3 = 3680 ± 190 cal/mole for individual methyl‐group librations and a V33 or V6 = − 280 ± 130 cal/mole term which couples the two methyl tops. Evaluation of additional Fourier constants in th...

Methyl Libration in Propane Measured with Neutron Inelastic Scattering

Electron configurations for the low excited states of the COOR radical (R = alkyl group or H atom) and the COO− ion are given. Their longest wave‐length absorptions are interpreted in terms of transitions to their lowest excited states. In the COOR radical this absorption comes at λ2100 and is weak. It is interpreted as due to a transition like that producing the weak region at λ2900 in the spectrum of the >C = O group in aldehydes and ketones. The COO− ion appears to show an analogous weak absorption but this is largely covered by a much stronger region. The latter is interpreted as possibly due to a transition in which a non‐bonding oxygen electron is excited to an antibonding molecular orbital of the unsaturation or x type. This transition should be strong in the ion, probably is weak in the acids and esters, and is entirely absent in the aldehydes and ketones. Possible interpretations of the λ1700 absorption in acids and esters are briefly discussed.

Henry L. McMurry

Papers

The Long Wave‐Length Spectra of Aldehydes and Ketones Part II. Conjugated Aldehydes and Ketones

Methyl Libration in Propane Measured with Neutron Inelastic Scattering

The Long Wave‐Length Spectra of Saturated Carboxylic Acids, Esters, and Salts