Accurate ab initio density fitting for multiconfigurational self-consistent field methods

Using Cholesky decomposition and density fitting to approximate the electron repulsion integrals, an implementation of the complete active space self-consistent field (CASSCF) method suitable for large-scale applications is presented. Sample calculations on benzene, diaquo-tetra-mu-acetato-dicopper(II), and diuraniumendofullerene demonstrate that the Cholesky and density fitting approximations allow larger basis sets and larger systems to be treated at the CASSCF level of theory with controllable accuracy. While strict error control is an inherent property of the Cholesky approximation, errors arising from the density fitting approach are managed by using a recently proposed class of auxiliary basis sets constructed from Cholesky decomposition of the atomic electron repulsion integrals.     

On the accuracy of higher-order force constants calculated at the self-consistent field level of theory

Cubic and quartic internal coordinate force constants are often obtained by a least-squares fit of a set of ab initio energies to an expansion of the potential energy. The reliability of such a procedure can now be determined, since analytic Cartesian cubic force constants are available which, when used in a finite difference procedure, also yield ab initio Cartesian quartic force constants. It is shown that unless the points of the energy grid are situated close to the equilibrium point unreliable results are obtained. This is why ab initio SCF anharmonic constants are more accurate than previously believed.     

The problem of hole localization in inner-shell states of N2 and CO2 revisited with complete active space self-consistent field approach

Potential energy curves for inner-shell states of nitrogen and carbon dioxide molecules are calculated by inner-shell complete active space self-consistent field (CASSCF) method, which is a protocol, recently proposed, to obtain specifically converged inner-shell states at multiconfigurational level. This is possible since the collapse of the wave function to a low-lying state is avoided by a sequence of constrained optimization in the orbital mixing step. The problem of localization of K-shell states is revisited by calculating their energies at CASSCF level based on both localized and delocalized orbitals. The localized basis presents the best results at this level of calculation. Transition energies are also calculated by perturbation theory, by taking the above mentioned MCSCF function as zeroth order wave function. Values for transition energy are in fairly good agreement with experimental ones. Bond dissociation energies for N(2) are considerably high, which means that these states are strongly bound. Potential curves along ground state normal modes of CO(2) indicate the occurrence of Renner-Teller effect in inner-shell states.     

The generalized active space concept in multiconfigurational self-consistent field methods

A multiconfigurational self-consistent field method based on the concept of generalized active space (GAS) is presented. GAS wave functions are obtained by defining an arbitrary number of active spaces with arbitrary occupation constraints. By a suitable choice of the GAS spaces, numerous ineffective configurations present in a large complete active space (CAS) can be removed, while keeping the important ones in the CI space. As a consequence, the GAS self-consistent field approach retains the accuracy of the CAS self-consistent field (CASSCF) ansatz and, at the same time, can deal with larger active spaces, which would be unaffordable at the CASSCF level. Test calculations on the Gd atom, Gd(2) molecule, and oxoMn(salen) complex are presented. They show that GAS wave functions achieve the same accuracy as CAS wave functions on systems that would be prohibitive at the CAS level.     

First-Order geometrical response equations for state-averaged multiconfigurational self-consistent field (SA-MCSCF) wave functions

The first-order geometrical response equations for a state-averaged multiconfigurational self-consistent field (SA -MCSCF ) calculation are derived. This derivation is carried through from first principles to final working equations suited for computer implementation. The final equations are expressed such that the energies and wave functions must be known only for the internal SA -MCSCF states. In the derivation, the special but important case where two or more internal states have equal weighting factors is treated in a manner fully consistent with all other cases. Except for introducing extra equations that are straightforward to solve, the case where two or more internal states have equal weighting factors introduces no new complications.     

Observation of inner-shell triplet states of CO2 and N2O and of inner-shell fine structure in Kr and Xe

Inner-shell singlet-triplet transitions in CO₂ and N₂O have been observed by the electron energy-loss technique at low values of the incident electron energy, typically 1.4 times the excitation energies of the states. The same technique has been used to observe fine structure in transitions near the M_4.5 edges in Kr and the N_4.5 edges in Xe.     

Interpretation of multiconfigurational states in the wave-operator method

We discuss methods of analyzing arbitrary wave functions, such as those for the total configuration interaction. We introduce the collectivity number as an invariant characteristic of the multiconfigurational character of the state. We determine the maximum value of the collectivity which can occur in the dissociative state. It is shown that in conjugated systems the weights of the valence structure of different ionic characters (polarities) approximately follow a binomial distribution. The ionic and covalent character indices of an atom are defined and a connection is established between these indices and the spin correlation functions, for which a sum rule is found.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 5, pp. 513–535, September–October, 1990.     

A self-consistent field procedure for stationary states using an algebraic approach and the maximum entropy formalism

A stationary state of maximal entropy is derived as a solution of a variational procedure. Generators of a continuous group are used as the constraints. The self-consistent hamiltonian is linear in these generators so that the solution of the self-consistency problem is replaced by a solution of an algebraic equation. The familiar Hartree-Fock procedure is a special case.     

Hamiltonian for the orbitals of general multiconfigurational self consistent field wave functions

The variational conditions for the orbitals of general multiconfigurational SCF wave functions are coupled in a unique way to construct a one-electron Hamiltonian with which one can determine all the occupied orbitals. Properties and application of the one-electron Hamiltonian in the relativistic framework are also discussed.     

Ground and lowest-lying electronic states of CoN. A multiconfigurational study

The lowest-lying X1Sigma+, a3Phi, b3II, c5Delta, A1Phi, and B1II electronic states of CoN have been investigated at the ab initio MRCI and MS-CASPT2 levels, with extended atomic basis sets and inclusion of scalar relativistic effects. Among the singlet states, the A1Phi and B1II states have been described for the first time. Potential energy curves, excitation energies, spectroscopic constants, and bonding character for all states are reported. Comparison with other early transition-metal nitrides (ScN, TiN, VN, and CrN), isoelectronic (NiC) and isovalent (RhN and IrN) species has been made, besides analyzing the B1II <=> X1+ electronic transition in terms of Franck-Condon factors, Einstein coefficients, and radiative lifetimes. At both levels of theory, the following energetic order has been obtained: X1Sigma+, a3Phi, b3II, c5Delta, A1Phi, and B1II, with good agreement with experimental results. In contrast, previous DFT and MRCI calculations predicted the ground state to be the 5Delta state.     

Potential energy curves and spectral properties for electronic states of F2 and F+2

Potential energy (PE) curves for the Rydberg states of F₂, and for the ground and lowest two electronic states each of symmetry ²Π_g,u, ²Δ_g,u and ²Σ^±_g,u of F⁺₂, have been obtained using modest-sized configuration-interaction calculations. These PE curves have been used to calculate spectroscopic constants for the electronic states and the results agree reasonably well with the limited experimental and theoretical results previously reported. The theoretical PE curves for the Rydberg states of F₂ are found to be strongly perturbed by valence-Rydberg-ionic interactions and these perturbations appear to be responsible for certain features in recently reported electron energy-loss spectra in F₂. The corresponding electronic wavefunctions have been used to calculate the electronic transition moment, as a function of the internuclear distance, for dipole-allowed transitions between the lowest excited electron state of each symmetry and the appropriate ground electronic state. The radiative emission probabilities, natural lifetimes, and absorption oscillator strengths, for each band system, are also reported here. The predicted lifetimes for vibrational levels of the A ²Π_u of electronic state in F⁺₂ vary from 1.3–1.5 μs and agree reasonably well with the single available set of measurements. The predicted radiative lifetimes for the higher electronic states of F⁺₂ are substantially longer and fall into the range 5–100 ms.     

Basis set selections for relativistic self-consistent field calculations

Practical methods of generating reliable and economic basis sets for relativistic self-consistent fields (RSCF) calculations are developed. Large component basis sets are generated from constrained optimizations of exponents in the nonrelativistic atomic calculations for light atoms. For heavy atoms, large component basis sets for inner core orbitals are generated by fitting numerical atomic spinors of Dirac-Hartree-Fock calculations with appropriate number of Slater-type functions. Small component basis sets are obtained by using the kinetic balance condition and other computational criteria. With judicious selections of the basis sets, virtual orbitals in RSCF calculations become very similar to those in nonrelativistic calculations, implying that relativistic virtual orbitals can be used in electron correlation calculations in the same manner as the conventional nonrelativistic virtual orbitals. It is also evident that the Koopmans' theorem is also valid in RSCF results.     

New vibrational self-consistent field program for large molecules

A recently developed, general computer program that performs vibrational self-consistent field (VSCF) calculations for large molecules is described. The program, which we refer to as VSCF―95, requires as its only input a force field in mass-scaled normal coordinates. Currently, it is limited to a maximum of 200 normal modes, and the force field is limited to coupling terms involving a maximum of six normal modes, with a maximum order of six in any normal mode. As output the program returns VSCF energies for specified quantum states. We illustrate the code with two new applications. The first is to HCO, for which we use a full sixth-order force field. The second is to a model of the fullerene, C₆₀, for which we have calculated a 75,731-term force field, which includes all anharmonic terms up to fifth order, and all two-mode coupling terms up to fourth order. © 1996 by John Wiley & Sons, Inc.     

Simplified time-dependent self-consistent field approximation for intramolecular dynamics

The time-dependent Hartree approximation is applied to intramolecular dynamics of polyatomics with smooth, locally quadratic potential surfaces. It is shown that the full quantum solution is obtained from a certain single self-consistent trajectory. An extremely simple model results, pertinent to intramolecular energy transfer, vibrational lineshapes and unimolecular decay.     

Potential use of the activation energy value calculated from the thermoluminescence glow curves to detect irradiated food

We herein report on the calculation of the activation energy (E _a) from the thermoluminescence (TL) glow curves performed by the initial rise method that allows us to discriminate between irradiated and non-irradiated sesame seeds. E _a values of natural TL (0.68 ± 0.03 eV) and gamma-induced TL (never lower than 0.82 ± 0.02 eV) appear as a complementary criterion to be used differentiating between irradiated and non-irradiated foodstuffs with the position and the intensity of the main peak of the TL emission. In addition, E _a values taken from irradiated sesame samples at different doses (1, 5 and 10 kGy) and stored up to 15 months after being processed were compared to a ‘positive’ Spanish blend (i.e. at least one component was commercially irradiated).