With the increasing availability of powerful computers, attempts to calculate the electronic structure and properties of molecules by the direct ab initio solution of a many-body Schrodinger equation have received a great stimulus. The authors review the mainstream developments in quantum chemistry and give a straightforward account of some of the many-body techniques borrowed, with appropriate modifications, from other areas of physics-field theory, nuclear theory and solid-state theory. After a historical introduction, the traditional approach based on the self-consistent field and the method of configuration interaction is developed in detail. This is followed by the introduction of the cluster expansion, various types of correlated electron-pair theory, and diagrammatic perturbation methods. Finally, propagator and Green function techniques are reviewed, not only as a means of calculating transition energies but also as an alternative approach to the determination of the electronic ground state.

http://iopscience.iop.org/article/10.1088/0034-4885/43/9/001/pdf

Quantum theory of molecular electronic structure

Due to formal and computational advances in coupled-cluster theory over the past few years, it is now possible to obtain very accurate molecular geometries, vibrational frequencies, heats of formation, binding energies, and vertical electronic excitation energies. For example, based on statistical analyses of a large number of calculations, it is shown that the CCSD(T)/spdfg level of theory gives rXH,rXY (double bonds), and rXY (triple bonds) with an average error of 0.0010, 0.0020, and 0.0026 A, respectively, with the theoretical bond distances usually too long relative to experiment. This level of theory yields bond angle predictions that are too small by 0.21 degrees on average. Fundamental vibrational frequencies predicted at the CCSD(T)/spdfg level of theory are accurate to better than 8.0 cm-1 on average, but the remaining errors are less systematic than those found for the geometrical parameters, except for X–Y stretches which are usually underestimated relative to experiment. For molecules described reasonably well by a single determinant reference function, single- and multiple-bond energies are given to within 1.0 and 2.0 kcal/mol, respectively, at the CCSD(T)/spdfg level of theory. The present monograph reviews the advances that have lead to the current state-of-the art, and also summarizes selected examples from the published literature.

Achieving Chemical Accuracy with Coupled-Cluster Theory

The atomic characteristics, which govern changes in bonding properties due to relativistic effects in heavy atoms, are identified from a scattering theoretic standpoint. It is shown that within an all-electron calculation scalar relativistic corrections to valence orbitals relevant to atomic bonding properties can be made via a local pseudopotential for all elements. The present approach reproduces molecular geometries and vibrational frequencies excellently for a test set of relatively simple molecules, where good experimental data are available. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 423–433, 1998

A scattering theoretic approach to scalar relativistic corrections on bonding

New correlation consistent basis sets based on both pseudopotential (PP) and all-electron Douglas-Kroll-Hess (DKH) Hamiltonians have been developed from double- to quadruple-zeta quality for the actinide atoms thorium and uranium. Sets for valence electron correlation (5f6s6p6d), cc − pV nZ − PP and cc − pV nZ − DK3, as well as outer-core correlation (valence + 5s5p5d), cc − pwCV nZ − PP and cc − pwCV nZ − DK3, are reported (n = D, T, Q). The -PP sets are constructed in conjunction with small-core, 60-electron PPs, while the -DK3 sets utilized the 3rd-order Douglas-Kroll-Hess scalar relativistic Hamiltonian. Both series of basis sets show systematic convergence towards the complete basis set limit, both at the Hartree-Fock and correlated levels of theory, making them amenable to standard basis set extrapolation techniques. To assess the utility of the new basis sets, extensive coupled cluster composite thermochemistry calculations of ThFn (n = 2 − 4), ThO2, and UFn (n = 4 − 6) have been carried out. After accurately accounting for valence and outer-core correlation, spin-orbit coupling, and even Lamb shift effects, the final 298 K atomization enthalpies of ThF4, ThF3, ThF2, and ThO2 are all within their experimental uncertainties. Bond dissociation energies of ThF4 and ThF3, as well as UF6 and UF5, were similarly accurate. The derived enthalpies of formation for these species also showed a very satisfactory agreement with experiment, demonstrating that the new basis sets allow for the use of accurate composite schemes just as in molecular systems composed only of lighter atoms. The differences between the PP and DK3 approaches were found to increase with the change in formal oxidation state on the actinide atom, approaching 5-6 kcal/mol for the atomization enthalpies of ThF4 and ThO2. The DKH3 atomization energy of ThO2 was calculated to be smaller than the DKH2 value by ∼1 kcal/mol.

Correlation consistent basis sets for actinides. I. The Th and U atoms

Verwendung einer neuer Methode zur Berechnung von Kraftkonstanten

High‐resolution spectra of the infrared‐active stretching fundamental ν3 of 238UF6 have been obtained between 620.6 and 633.5 cm−1 using tunable semiconductor diode lasers. Interference from hot bands was suppressed by cooling the UF6 in a supersonic expansion, and useful monomer concentrations were produced with effective temperatures of <100 K. Portions of the band from P(77) to R(66) are illustrated. All transitions from the vibrational ground state have been assigned, and the Q branch has been fully analyzed. A total of 43 line frequencies and 110 frequency differences extending in J to P(77), Q(91), and R(67) has been used to fit seven spectroscopic constants. The ground‐ and excited‐state values of the rotational constant B could be individually determined, and the U–F bond length in the ground vibrational state is r0=1.9962±0.0007 A. The Q branch of 235UF6 has also been analyzed and the 235UF6–238UF6 ν3 isotope shift measured to be 0.603 79±0.000 17 cm−1. The isotope shift and the Coriolis constant...

Measurement and analysis of the infrared‐active stretching fundamental (ν3) of UF6

Determination of the Two‐Dipole Moment Components in Nitrosyl Fluoride

Analysis of the rotational structure of ν1 and ν3 infrared bands of nitrosyl fluoride at 1844.03 and 765.85 cm−1 showed that this molecule is nearly a prolate symmetric top. The following rotational parameters based on symmetric‐top theory were found and are expressed in cm−1: for ν1, 2B″=0.7515, 2B′=0.7483, DJ′+DJ″=0.0000275; for ν3, 2B″=0.7521, 2B′=0.7503, DJ′+DJ″=0.00000236. The anharmonic term x33 was found to be −1.06 cm−1 from ν3. The anharmonic term x12 was found to be +1.03 cm−1 from ν1.

The Infrared Spectrum of Nitrosyl Fluoride. Part II. Rotational Analysis of ν1 and ν3

The dielectric constant of chlorine trifluoride was determined at 9400 mc/sec by measuring the change in the resonant frequency of a cavity when it is filled with the vapor. Corrections were made for the amount of dimer formed. The monomer molar polarization was best represented by P=15.944+1882.0/T°K cc and the dipole moment was 0.554 Debye unit. The average dimer molar polarization was found to be 49.8 cc assuming no dipole moment.

Dale W. Magnuson

Papers

Measurement and analysis of the infrared‐active stretching fundamental (ν3) of UF6

Determination of the Two‐Dipole Moment Components in Nitrosyl Fluoride

The Infrared Spectrum of Nitrosyl Fluoride. Part II. Rotational Analysis of ν1 and ν3

Dielectric Constant Measurements of Chlorine Trifluoride at 9400 mc/sec

The Dielectric Constant of Uranium Hexafluoride Vapor at 9400 mc/sec