Complete Active Space SCF Level Research Articles

A dynamic correlation dressed complete active space method: Theory, implementation, and preliminary applications.

Complete Active Space SCF (CASSCF) theory may provide poor 0th order descriptions due to the lack of dynamic correlation. The most popular post-CASSCF approaches for recovering dynamic correlation are methods which keep the configuration interaction coefficients fixed at the CASSCF level and use internal contraction. This may result in severe inaccuracies where the wavefunction changes considerably under the influence of dynamic correlation. In this paper, we propose and compare several variants of a straightforward method of the "perturb-then-diagonalize" type that is aimed at keeping this balance while remaining computationally tractable and numerically stable. The method is loosely based on the theory of intermediate Hamiltonians and has been given the acronym "dynamic correlation dressed CAS" (DCD-CAS), with the second-order treatment, DCD-CAS(2), being the most practically useful member of the family. The dynamic correlation energy is treated to second order with a 0th order Hamiltonian based on Dyall's Hamiltonian. The method is orbitally invariant with respect to unitary transformations in the occupied, active, and virtual subspaces. It yields the ground- and low-lying excited states at the same time. Detailed numerical evaluations show that DCD-CAS(2) is superior to NEVPT2 for the difficult situations mentioned above while being very close to it when CASSCF provides a good 0th order description.

On the stability of Be3: A benchmark complete active space self-consistent field + averaged quadratic coupled cluster study

The optimized geometries and binding energies for the linear and triangular isomers of the beryllium trimer have been obtained through benchmark multireference averaged quadratic coupled cluster (AQCC) calculations using very large complete active space SCF (CASSCF) references (12 active electrons in 13 and 14 orbitals). Geometries were optimized with the cc-pV5Z basis, while the binding energies (including counterpoise correction) were obtained with the significantly larger aug-cc-pV5Z basis set. The binding energies (27.3 and 16.3 kcal/mol for the equilateral and linear isomers, respectively) are larger than the previous full CI benchmark values, while the corresponding Be-Be equilibrium distances of 4.101 and 4.088 a.u. are smaller. In view of the near-size consistency character of the CASSCF + AQCC method, the fact that all 12 electrons are fully correlated, the active reference space includes 14 orbitals, and the very large basis set used here, we propose to consider these results as reference data for Be(3). Using the electron pair localization function obtained at the CASSCF(12,15) level, it is clearly illustrated that the 2p orbitals lying in the molecular plane play a dominant role in the bonding pattern for the equilateral isomer.

Photodissociation of HN3 at 248 nm and Longer Wavelength: A CASSCF Study

In the present work, photodissociation of HN3 at 248 nm and longer wavelength is investigated with the complete active space SCF (CASSCF) molecular orbital method. The stationary points on the ground- and excited-state potential energy surfaces are fully optimized at the CASSCF level with cc-pVDZ and cc-pVTZ basis sets. The potential energy profiles, governing HN3 dissociation to NH + N2 and H + N3, are characterized with the multireference MP2 (CASPT2) algorithm. The pathways leading to different products are determined on the basis of the obtained potential energy surfaces of dissociation and their crossing points. A comparison is made among the present and previous theoretical results and experimental findings. The present study provides an insight into the mechanism of the UV photodissociation of HN3 at a wavelength range from 355 to 248 nm.

Ab initio calculation of potential energy surfaces for the three lowest triplet states (1 3A′′,1 3A,2 3A′′) of PH(X,A)–He

Quantum chemical ab initio calculations at the complete active space SCF level and with inclusion of correlation effects have been performed for the potential energy surfaces of PH in its X 3Σ− ground state and its first excited triplet state, A 3Π, colliding with He atoms. The PH distance was fixed at its experimental value (of the A 3Π state), the PH–He distance and the HePH angle were varied. All three potential energy surfaces [1 3A′′ for PH(X)–He and 1 3A,2 3A′′ for the two components of PH(A)–He] are purely repulsive, except for very shallow van der Waals minima with well depths of about 15–40 cm−1. The interaction potentials decay approximately exponentially with increasing PH–He distance and show large angular anisotropies. Legendre expansions for the angular dependence of the potential surfaces converge slowly for V(1 3A′′) and the sum potential 1/2[V(2 3A′′)+V(1 3A)], but rapidly for the corresponding difference potential 1/2[V(2 3A′′)−V(1 3A)]. The present PH(A)–He potentials have been used in the companion paper by Neitsch et al. [J. Chem. Phys. 106, 7642 (1997)], for the calculation of thermal state-to-state rate constants for inelastic PH(A)–He collisions.

The structure and energetics of B3N2, B2N3, and BN4

The structures of B3N2, B2N3, and BN4 have been investigated using complete active space SCF (CASSCF) and augmented coupled cluster (CCSD(T)) methods. B3N2 has a symmetry-broken linear ground state structure BNBNB(2Σ+) and is very stable. B2N3 has a linear ground state structure BNBNN(2Π) and is nearly isoenergetic with its (thermodynamically preferred but symmetry forbidden) dissociation products BNB(2Σ+) + N2(1Σg +). BN4 has the ground state structure NNBNN(2Πu) that is symmetry broken at the CCSD(T), but symmetric at the CASSCF level. Predictions for the infrared spectrum of the species involved have been given. The best computed total atomization energies ΣD e (error bar ±4 kcal mol-1) are: B3N2, 504·6 kcal mol-1; B2N3, 479·1 kcal mol-1; and BN4, 460·8 kcal mol-1.

On the structure of the 3B 1 excited state of water

Ab initio calculations using several large basis sets at the unrestricted (U) and projected (P) Hartree-Fock (HF) and second-order Møller-Plesset (MP2) levels have been performed on the lowest triplet excited state ( 3B 1) of C 2v water. It was found that the unrestricted SCF calculations are able to produce geometries, dipole moments and dipole polarizabilities in agreement with available complete active space (CAS) SCF calculations, if sufficiently extended basis sets are used. The smaller basis sets used in this work (6-31 + G(d,p), +VP S(2d) S, +VP S(3d) S and atomic natural orbital (ANO)) predicted a linear equilibrium geometry instead of the CAS SCF bent one. Adiabatic excitation energies, however, are not in good agreement with those at the CAS SCF level even for large basis sets, unless dynamic correlation effects (at the MP2 level) are taken into account. Optimum geometries at this level are also in better agreement with these CAS SCF ones. However, analysis of the force-constant matrix showed the presence of a large negative eigenvalue. The associated eigenvector shows that the optimum C 2v structure is a transition state towards dissociation in OH( 2Π) + H. A potential energy surface was then built for the C 2v structure varying both the bond length and the bond angle at the PHF, UMP2 and PMP2 levels with the 6-311++G(2d,2p) basis set. No other minimum than the present one and the previously reported asymptotic limit O( 3 P) + H 2( 1Σ +) were found. At the PHF level, the linear D ∝ h structure behaves like a minimum, but it turns out as a transition state at the more accurate PMP2 level. All the critical points on the UMP2 surface were directly located with several of the larger basis sets and their relative energies are reported. Generally speaking, PMP2 and UMP2 calculations are in agreement, implying that spin-contamination is not imported in determining the characteristics of this surface. Moreover the vertical and adiabatic excitation energies from the ground 1A 1 state are in agreement with the CAS SCF calculations. However, the results for the critical points on the surface are not in quantitative agreement with a previous CIPSI study. The results found imply also that the 3B 1 state is dissociative, as shown by a potential energy surface built around the bent C 2v structure but relaxing the geometry constraint.

Bifurcation analysis in terms of second-order Jahn—Teller effect

It is known that the reaction path for the dissociation reaction H 2CS → H 2 + CS has C s symmetry while the reaction path for the isomerization reaction H 2CS → HCSH has C 1 symmetry at the Hartree-Fock (HF) level. In addition, the former reaction path is known to have a bifurcating region. In order to clarify the bifurcation mechanism in terms of the second-order Jahn-Teller (SOJT) effect, the intrinsic reaction coordinates (IRCs) and energies of the first-excited state (A″) along the IRC were calculated for both reactions under the constraint of C s symmetry with 6–31G** basis sets at the HF level and at the complete active space SCF (CASSCF) level. At the HF level, bifurcation was proven to occur in both dissociation and isomerization reactions due to a vibronic interaction through the SOJT effect. At the CASSCF level, however, the energy separations between the ground and the A″ excited states in both reactions are large enough to avoid state intermixing due to the SOJT effect, and the bifurcation disappears from each IRC. For the purpose of comparison, the IRCs of H 2CO for the dissociation to H 2 + CO and for the isomerization to HCOH were also calculated with 6–31G** basis sets at the HF level. As expected from the SOJT theory for the calculated large energy separation, bifurcation does not occur in both dissociation and isomerization reactions of H 2CO.

Bifurcation analysis in terms of second-order Jahn-Teller effect

It is known that the reaction path for the dissociation reaction H 2CS → H 2 + CS has C s symmetry while the reaction path for the isomerization reaction H 2CS → HCSH has C 1 symmetry at the Hartree—Fock (HF) level. In addition, the former reaction path is known to have a bifurcating region. In order to clarify the bifurcation mechanism in terms of the second-order Jahn—Teller (SOJT) effect, the intrinsic reaction coordinates (IRCs) and energies of the first-excited state (A″) along the IRC were calculated for both reactions under the constraint of C s symmetry with 6–31G ** basis sets at the HF level and at the complete active space SCF (CASSCF) level. At the HF level, bifurcation was proven to occur in both dissociation and isomerization reactions due to a vibronic interaction through the SOJT effect. At the CASSCF level, however, the energy separations between the ground and the A″ excited states in both reactions are large enough to avoid state intermixing due to the SOJT effect, and the bifurcation disappears from each IRC. For the purpose of comparison, the IRCs of H 2CO for the dissociation to H 2 + CO and for the isomerization to HCOH were also calculated with 6–31G ** basis sets at the HF level. As expected from the SOJT theory for the calculated large energy separation, bifurcation does not occur in both dissociation and isomerization reactions of H 2CO.

Potential energy surfaces in hyperspherical coordinates: AB initio kinetic paths for the O( 3P)+H 2 reaction

The direct ab initio generation of potential energy surfaces for an elementary chemical reaction is discussed from the viewpoint of its use in dynamical calculations within the hyperspherical coordinate framework. An example is given of the reaction O( 3P)+H 2→OH+H, for which kinetic paths (valley bottoms and ridge) as a function of the kinetic radius are computed at the complete active space SCF level. Along the kinetic paths energies are refined using extensive multi-reference configuration interaction calculations.