Active Orbital Space Research Articles

Complete active space coupled-cluster method. Extension of single-reference coupled-cluster method using the CASSCF wavefunction

It is proposed that the calculation of non-dynamical electron correlation effects by the complete active space self-consistent field (CASSCF) method can be extended by the inclusion of dynamical correlation effects through the use of a suitably modified single-reference coupled-cluster (CC) procedure. The CASSCF method supplies the reference configuration and the complete set of the CC amplitudes corresponding to the space of active orbitals. These amplitudes are then fed into the CC procedure to determine the CC amplitudes of low rank, but corresponding to the full orbital space. The proposed CASCC method combines the formal simplicity of the single-reference CC method with the flexibility of the CASSCF approach, but is limited to cases where there is a single configuration with the highest weight in the CASSCF wavefunction.

Frequency-dependent polarizabilities and first hyperpolarizabilities of H2O

Static and frequency-dependent dipole polarizabilities α and first hyperpolarizabilities β are calculated for H2O using self-consistent field (SCF) and multiconfigurational self-consistent- field (MCSCF) linear and quadratic response theory. With an active orbital space where one correlating orbital is included for each occupied valence orbital excellent agreement is obtained with the experimental hyperpolarizability. Basis set dependency has been investigated and a detailed vibrational analysis has been carried out.

Frequency-dependent polarizabilities and second hyperpolarizabilities of N 2

The static- and frequency-dependent dipole polarizabilities α and second hyperpolarizabilities γ of N 2 are calculated at different wavelengths using self-consistent field and multiconfigurational self-consistent field linear and quadratic response theory. Electron correlation is found to be important. With an active orbital space consisting of one correlating orbital for each occupied valence orbital excellent agreement is obtained with the experimental polarizabilities and hyperpolarizabilities. The dispersion of the hyperpolarizability which previously has been determined from electric-field-induced second harmonic generation experimental data is shown to give an inaccurate description in the low frequency region due to lack of flexibility in the fitting function. Our results stress that it is important to carry out calculations at frequencies where experiments are carried out to avoid extrapolation to the static limit. Basis set effects have been investigated. f functions are important whereas g functions have little effect. The vibrational averaging has been found to be of little importance.

A restricted active space SCF study of the lifetime of the A3Π state of SH+

Restricted active space (RAS) SCF calculations have been performed on the potential curves for the X3Σ- and A3Π states of the SH+ ion and on the lifetime of the v′ = 0,1 vibrational levels of the A state. The convergence of the transition moment integral as a function of the size of the active orbital space was used to select the active orbitals. The calculated value of the v′ = 0 lifetime is 1·1 µs. An estimate of the errors remaining in the calculation leads to a final theoretical value of 1·07 ± 0·13 µs. Computed bond distances and bond energies are 1·367 (1·364) Å and 3·46 (3·70)eV, respectively, for the X state, and 1·502 (1·501) Å and 1·64 (1·78)eV, respectively, for the A state (experimental values within parentheses).

Spin–orbit coupling constants in a multiconfiguration linear response approach

Spin–orbit coupling constants between singlet and triplet states are evaluated as residues of multiconfiguration linear response functions. In this approach, the spin–orbit coupling constants are automatically determined between orthogonal and noninteracting states. Sample calculations are presented for the X 3Σ−g–b 1Σ+g transition in O2 and the 1A1–3B1 transition in CH2. The convergence of the coupling constants is examined as a function of basis set and level of correlation. An exotic behavior is observed in the correlation of the 1A1 state for CH2 when increasing the active space, demonstrating an intricate coupling between the dynamic and static correlation. In general, the results indicate that reliable spin–orbit coupling constants between valence states may be obtained with a 4s3p2d1f basis set for first row atoms and a modest active orbital space.

A restricted active space self-consistent field and multireference configuration interaction study of the lifetime of the A 3Π state of SO

A b initio methods were applied to compute the potential curves for the X 3Σ− and A 3Π states, the transition dipole moment, and the radiative lifetimes of the vibrational levels of the A state of the SO molecule. Extended atomic natural orbital basis sets including up to g-type functions were used. The potential energy curves were computed at the multireference configuration interaction level of approximation. The calculated bond distances and bond energies are 1.498 (1.481) Å and 5.21 (5.36) eV, respectively, for the X state, and 1.694 (1.609) Å and 0.57 (0.64) eV, respectively, for the A state (experimental values within parentheses). Restricted active space self-consistent field (RASSCF) wave functions were used to obtain the transition dipole moments, and the size of the RASSCF active orbital space was increased until stability of the transition moment value was achieved. The calculated transition moment strongly depends on the internuclear distance. The calculated value of the A 3Π, v=0 lifetime is 46.6 μs, while the experimental values are in the range of 36–39 μs. The computed lifetime is a very sensitive function of the relative accuracy of the potential energy and transition moment curves: for example, removing the g-type function on sulphur increases the lifetime to 55 μs.

A restricted active space (RAS) SCF study of the lifetime of theA 3? state of OH+

Restricted Active Space (RAS) SCF calculations have been performed of the potential curves for theX3Σ− andA3Π states of the OH+ ion and on the lifetime of thev=0−2 vibrational levels of theA state. The convergence of the transition moment integral as a function of the size of the active orbital space was used to select the active orbitals. The calculated value of thev=0 lifetime is 2.4 µs. An estimate of the errors remaining in the calculation leads to a final theoretical value of 2.7±0.1 µs. Computed bond distances and bond energies are 1.031 (1.029) A and 5.05 (5.01) eV, respectively, for theX state, and 1.137 (1.135) A and 1.57 eV, respectively, for theA state (experimental values within parenthesis).

Theoretical study of the dipole moment function of OH(X 2Π)

We present a theoretical study of the sensitivity of the dipole moment function (DMF) of the X 2Π ground state of OH to basis set saturation and to refinements in the correlation treatment. Emphasis is placed on determining the slope of the DMF at re and the r value at which the maximum occurs. We consider the effect of oxygen polarization functions up through h type, expansion of the active orbital space to include the O 3dδ orbital, the effect of higher excitations using the averaged coupled-pair functional method, and the effect of evaluating the dipole moment as an energy derivative rather than as an expectation value. Our theoretical DMFs, which should be the most accurate to date, differ markedly from an empirical DMF of Turnbull and Lowe that is based on experimentally derived intensity ratios. The theoretical DMFs agree better with a recently published DMF of Nelson et al., but suggest that this empirical DMF is also inaccurate for r>2.3 a0.

Excitation energies, transition moments and dynamic polarizabilities for CH +. A comparison of multiconfigurational linear response and full configuration interaction calculations

Using a split valence with diffuse and polarization functions full configuration interaction excitation energies, transition moments and polarizabilities have been calculated for CH +. Comparisons have been made with multiconfiguration linear response calculations for various active orbital spaces and the active orbital space that gives results close to the full configuration interaction limit has been established.

A systematic approach to transition moment calculations

Extensive configuration interaction (CI) and multiconfiguration self-consistent-field (MCSCF) calculations on the A–X transitions of CH and CH+ are reported, which show how the transition dipole matrix element between two electronic states of a molecule can be determined accurately and systematically by a sequence of ab initio calculations. Two different computational approaches are investigated: one uses different orbitals for the two states involved and the other uses the same orbitals for both states. Both methods are shown to converge rapidly when the active orbital space is increased in such a way that all orbitals of similar importance are included at the same time. It is also shown that natural orbital occupation numbers from second-order CI calculations using a valence active orbital space provide an useful guide to the relative importance of natural orbitals; all orbitals of comparable occupation numbers must be included together.

An MC SCF study of the nucleophilic addition of OH − to ethene and formaldehyde

MC SCF computations on the nucleophilic addition of OH − to ethene and formaldehyde are presented. The active orbital space in the MC SCF computation is chosen in such a way that the OH lone pair can be represented by two different spatial orbitals so that the two lone-pair electrons can either be spin coupled together as a conventional lone pair, or one of the lone-pair electrons can be spin coupled to one of the π orbitals of the double bond. This removes the implicit constraint (present in an SCF computation) that the reaction must involve a heterolytic charge transfer. The energetics and geometries at the MC SCF level are quite different from SCF theory.

An extended-valence MC SCF procedure: determination of the dissociation energies of C 2, N 2, O 2, and F 2

A series of MC SCF calculations have been carried out on C 2, N 2, O 2, and F 2 with the goal of obtaining compact wavefunctions which recover a significant fraction of the electron correlation effects important for bond dissociation. The active orbital space is varied in size, with the largest spaces including the molecular orbitals derived from 2s, 2p, 3s, 3p and 4p atomic orbitals. Several basis sets ranging in size from 5s3p to 5s4p2d1f are investigated to determine the flexibility in the basis set needed with various choices of the active orbital space. The best extended-valence MC SCF (EVMC) dissociation energies are 0.2–0.5 eV less than the experimental values, indicating that further enlargement of the active orbital space is necessary to achieve 0.1 eV accuracy in the computed dissociation energies. The EVMC calculations reveal that, for the calculation of the dissociation energies, inclusion of non-valence orbitals is much more important for O 2 and F 2 than for C 2 and N 2. The EVMC results are compared with the predictions of full fourth-order perturbation theory, coupled cluster theory, and with the best available CI calculations.

The radiative lifetime of the A1Π state of CH+ calculated from long CAS SCF expansions

Abstract A theoretical study of the A 1 Π-X 1 Σ − transition of CH + is presented. Radiative lifetimes (τ) for the A state and the f ν′ν -(A–X) oscillator strengths are calculated, using long mutually non-orthogonal CAS SCF expansions. The convergence of these properties is studied with respect to the size of the active orbital space and the basis set. It is found that very large active spaces and basis sets are needed for obtaining reliably convergent results. The best calculated value for τ(ν′ = 0) of 850 ns and for f 00 of 5.45 × 10 −3 are in good agreement with the results from the most recent experimental investigation, 815 ± 25 ns and (5.66±0.20) × 10 −3 respectively. In the calculation use has been made of experimental excitation energies and potential curves. Compared to the previously most accepted lifetime the present theoretical and the recent experimental values demand an increase of the interstellar CH + abundance.

Core hole induced charge‐transfer reactions in disubstituted benzenes

AbstractThe application of the charge‐transfer concept on core electron ionization in donor–acceptor molecules is analyzed. A single excitation picture, involving the highest occupied and lowest unoccupied molecular orbitals is compared with a full π‐valence orbital active space model. The connections between the notion of charge transfer in donor–acceptor species with the shake‐up picture used for core photoelectron spectra of small molecules and with the dynamical screening concept applied on surface–adsorbate spectra are discussed.