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Analytic equations of the multiconfigurational SCF (MCSCF) response theory are combined with the finite-field (FF) approach to compute static and frequency dependent electric and magnetic properties of the Argon atom. A complete active space (CAS SCF) function including the 3s, 3p, 3d, 4s and 4p orbitals in the active space and a large (17s 13p 7d 5f 3g) basis set are employed. This permits an accurate determination of various linear and non-linear response properties such as e.g. electric dipole polarisability and second hyperpolarisability, Verdet constant, magnetisability and second hyperpolarisability. The results, both for the static values and for the frequency dependence of these properties, compare well with other most recent experimental and theoretical data.

The intrinsic reaction-path, reactants, transition state and products for the reaction of NH (3∑−)+H2 (1∑g+) → NH2 (2B1)+H (2S) involving the lowest triplet electronic state of NH3 were calculated using multi-configuration (MC) SCF methods. The calculated change of internal energy for the reaction of 11.0 kcal mol−1 agrees with the experimental value within 2 kcal mol−1. The barrier to reaction is 23.4 kcal mol−1 high. The harmonic MCSCF reaction-path potential was calculated and canonical variational transition state theory calculations of the rate constants performed over a temperature range from 400 to 2500 K. The computed rate constants are generally two orders of magnitude smaller than those of the comparable reaction of OH with H2, whereas those of the reverse reaction are by a factor of 20 larger than those of OH2 with H.

Ab initio calculations of parameters which characterize the NMR spectrum are presented for the cyclopropene molecule. The London orbitals CHF (or GIAO-CHF, Gauge-Independent Atomic Orbital Coupled Hartree-Fock) results for the shielding constants are in good agreement with the experimental data, accurately determined, and with otherab initio values. The calculations of the NMR spin-spin coupling constants have been performed using the Multiconfiguration Time-Dependent Hartree-Fock (MC TDHF) approach. Different basis sets and MC SCF wavefunctions were used to estimate the accuracy of the results. Good agreement is obtained with the coupling constants estimated using the available experimental data.

Gradient extremals define stream beds connecting stationary points on molecular potential energy surfaces. Using this concept we have developed an algorithm to determine transition states. We initiate walks at equilibrium geometries and follow the gradient extremals until a stationary point is reached. As an illustration we have investigated the mechanism for exchange of protons on carbon in methylenimine (H2C=NH) using a multi-reference self-consistent-field wave function.

When Moller-Plesset energy derivatives are determined in the canonical Hartree-Fock basis, singularities or instabilities may arise due to degeneracies among the occupied or unoccupied orbitals. If a non-canonical basis is used these singularities disappear. Numerically stable expressions are presented for the molecular gradient and Hessian of the second-order Moller-Plesset energy, obtained by differentiating a fully variational Lagrangian of the energy constructed in a non-canonical representation. By using a non-canonical representation, singularities and instabilities are avoided, and the variational property of the Lagrangian ensures that Wigner's 2n + 1 rule is satisfied for the orbital derivatives and that the multipliers satisfy the stronger 2n + 2 rule. It is shown that the most expensive step in the calculation of the Hessian scales as Mn 4o, where M is the number of independent Cartesian distortions, n the total number of orbitals, and o the number of occupied orbitals.

A configuration-interaction energy function (Lagrange) which is variational in all variables, including the orbital rotational parameters, is constructed. When this Lagrangian is used for obtaining configuration-interaction derivatives, all the important simplifications which occur for derivatives of variational wave functions carry over in a straightforward way. In particular, the state and orbital rotational response parameters obey the 2n+1 rule and the Lagrange multipliers obey the somewhat stronger 2n+2 rule. The simplifications which are normally obtained by invoking the Handy-Schaefer technique are automatically incorporated to all orders. Simple expressions for energy derivatives up to third order are presented. The relationship between the numerical errors in the variational parameters and the errors in the calculated energy derivatives is discussed.

Comparison is presented of energies, oscillator strengths, and polarization directions calculated using the dipole length and dipole velocity formulas for the lowest 4–7ππ* transitions in eight 6π-electron molecules of Cs symmetry using various amounts of CI, from singly excited configurations only (SCI) to complete CI (CCI), and also using the time-dependent Hartree-Fock (TDHF) method. The standard simple PPP approximation was used. For the strongest transitions, SCI and especially TDHF give results in fairly good agreement with CCI. For weaker transitions both SCI and TDHF give similar results, quite different from the CCI solutions. Rational methods for selecting a small number of configurations needed to reproduce correct order of excited states (SECI-1) or a somewhat larger number reproducing correct order, energies, oscillator strengths and polarization directions of transitions (SECI-2) are presented. Both, and particularly the latter, give similar results from both dipole length or dipole velocity formulas when Linderberg's relation is used for matrix elements of the linear momentum operator and in this respect resemble the TDHF and CCI methods for which both formulas necessarily give identical results.