rgen Aa. Jensen

Determinant based configuration interaction algorithms for complete and restricted configuration interaction spaces

A restricted active space (RAS) wave function is introduced, which encompasses many commonly used restricted CI expansions. A highly vectorized algorithm is developed for full CI and other RAS calculations. The algorithm is based on Slater determinants expressed as products of alphastrings and betastrings and lends itself to a matrix indexing C(Iα, Iβ ) of the CI vector. The major features are: (1) The intermediate summation over determinants is replaced by two intermediate summations over strings, the number of which is only the square root of the number of determinants. (2) Intermediate summations over strings outside the RAS CI space is avoided and RAS calculations are therefore almost as efficient as full CI calculations with the same number of determinants. (3) An additional simplification is devised for MS =0 states, halving the number of operations. For a case with all single and double replacements out from 415 206 Slater determinants yielding 1 136 838 Slater determinants each CI iteration takes ...

Multiconfigurational self‐consistent field calculations of nuclear shieldings using London atomic orbitals

Nuclear shielding calculations are presented for multiconfigurational self‐consistent field wave functions using London atomic orbitals (gauge invariant atomic orbitals). Calculations of nuclear shieldings for eight molecules (H2O, H2S, CH4, N2, CO, HF, F2, and SO2) are presented and compared to corresponding individual gauges for localized orbitals (IGLO) results. The London results show better basis set convergence than IGLO, especially for heavier atoms. It is shown that the choice of active space is crucial for determination of accurate nuclear shielding constants.

Quadratic response functions for a multiconfigurational self-consistent field wave function

We describe an efficient implementation of the quadratic response function for a multiconfiguration self‐consistent field reference wave function. The quadratic response function determines the hyperpolarizability and its residues determine the two‐photon transition matrix elements and the transition matrix elements between excited states. We report sample calculations for the hyperpolarizability of Ne and for the two‐photon transition matrix elements of Ne and H2.

Coupled cluster energy derivatives. Analytic Hessian for the closed-shell coupled cluster singles and doubles wave function: Theory and applications

Expressions for coupled cluster molecular energy derivatives up to third order are presented and the molecular gradient and Hessian are implemented in a computer code for the CCSD wave function. Sample calculations on water and hydrogen peroxide indicate that significant savings are obtained by calculating the Hessian analytically rather than by finite differences.

Hartree–Fock limit magnetizabilities from London orbitals

Molecular magnetizabilities have been calculated at the Hartree–Fock level for a series of diamagnetic molecules: H2O, NH3, CH4, PH3, H2S, CO2, CSO, CS2, and C3H4. Gauge invariance is imposed by the use of London atomic orbitals. The results are compared to those obtained with the IGLO (individual gauge for localized orbitals) method and are found to converge faster to the basis set limit. Magnetizabilities obtained from basis sets of different quality never differ by more than 4% for the London method, compared to 20% for IGLO. The Hartree–Fock limit may be approached using London basis sets of moderate size, in contrast to calculations of molecular polarizabilities which require large basis sets to be reliable. Comparison with experiment shows that the Hartree–Fock method overestimates experimental susceptibilities by 5%–10%.

A multiconfigurational self‐consistent reaction‐field method

We present theory and implementation for a new approach for studying solvent effects: the multiconfigurational self‐consistent reaction‐field (MCSCRF) method. The atom, molecule, or supermolecule is assumed to be surrounded by a linear, homogeneous, continuous medium described by its macroscopic dielectric constant. The electronic structure of the compound is described by a multiconfigurational self‐consistent field (MCSCF) wave function. The wave function is fully optimized with respect to all variational parameters in the presence of the surrounding polarizable dielectric medium. We develop a second‐order convergent optimization procedure for the solvent states. The solvent integrals are evaluated by an efficient and general algorithm. The flexible description of the electronic structure allows us to accurately describe ground, excited, or ionized states of the solute. Deficiencies in the calculation can therefore be assigned to the cavity model rather than the description of the solute.

Near-resonant absorption in the time-dependent self-consistent field and multiconfigurational self-consistent field approximations

Computationally tractable expressions for the evaluation of the linear response function in the multiconfigurational self-consistent field approximation were derived and implemented. The finite lif ...

Gauge‐origin independent multiconfigurational self‐consistent‐field theory for vibrational circular dichroism

Multiconfigurational self‐consistent‐field (MCSCF) theory is presented for the gauge‐origin independent calculation of vibrational circular dichroism. Origin independence is attained by the use of London atomic orbitals (LAO). MCSCF calculations on ammonia and its isotopomer NHDT demonstrate that atomic axial tensors and vibrational rotational strengths converge fast with the size of the basis set when LAOs are used. The correlation effects are significant both for the atomic tensors and the vibrational rotational strengths even for the single configuration dominated NHDT molecule.

Indirect nuclear spin–spin coupling constants from multiconfiguration linear response theory

We have used multiconfiguration self‐consistent‐field theory to determine indirect nuclear spin–spin coupling constants. The Fermi contact, spin dipole, and paramagnetic spin–orbit contributions are evaluated as multiconfiguration linear response functions at zero frequency and the diamagnetic spin–orbit contribution as an average value of the multiconfiguration wave function. Sample calculations on HD and CH4 demonstrate that most of the correlation contributions can be recovered in relatively small complete active space (CAS) reference state calculations.

Second‐order Mo/ller–Plesset perturbation theory as a configuration and orbital generator in multiconfiguration self‐consistent field calculations

It is shown that the magnitude of the natural orbital (NO) occupation numbers of second‐order Mo/ller–Plesset (MP2) perturbation theory can be used to select physically reasonable configuration spaces for ground state MCSCF calculations. When the MP2 NO’s are used as an initial guess for the orbitals, a second‐order Newton–Raphson MCSCF calculation is in the local region from the first iteration. Fast convergence is therefore ensured to a stationary point with orbitals of similar structure as the MP2 NO’s, thereby reducing significantly the risk of converging to undesired stationary points.