State-averaged Multiconfiguration Self-consistent Field Research Articles

Theoretical investigation of the dissociation of bridged disilyne

The dissociation potential energy surfaces of ground-state bridged disilyne ( 1A 1), the Si 2H 2 global minimum, is investigated using the state-averaged multi-configuration self-consistent field (SA-MCSCF) method. The dissociation energy of bridged disilyne into Si 2 ( 1Δ g+H 2( 1Σ + g) is predicted to be 42 kcal/mol. The very small calculated energy barrier (about 1 kcal/mol) given by the SA-MCSCF calculations disappears at the first-order configuration interaction level of theory. The spin-orbit coupling constant between the lowest 1A 1 and 3B 1 states is estimated to be about 60 cm −1 in the crossing region of their potential energy surfaces.

First-order nonadiabatic coupling matrix elements from multiconfigurational self-consistent-field response theory

A new scheme for obtaining first-order nonadiabatic coupling matrix elements (FO-NACME) for multiconfigurational self-consistent-field (MCSCF) wave functions is presented. The FO-NACME are evaluated from residues of linear response functions. The residues involve the geometrical response of a reference MCSCF wave function and the excitation vectors of response theory. Advantages of the method are that the reference state is fully optimized and that the excited states, represented by the excitation vectors, are strictly orthogonal to each other and to the reference state. In a single calculation the FO-NACME between the reference state and several excited states may be obtained simultaneously. The method is most well suited to describe situations where the dominant configurations for the two states differ mainly by a single electron replacement. When the dominant configurations differ by two electrons many correlating orbitals are required in the MCSCF reference state calculation to accurately describe the FO-NACME. FO-NACME between various states of H2, MgH2, and BH are presented. These calculations show that the method is capable of giving quantitatively correct results that converge to the full configuration interaction limit. Comparisons are made with state-averaged MCSCF results for MgH2 and finite-difference configuration interaction by perturbation with multi-configurational zeroth-order wave function reflected by interactive process (CIPSI) results for BH.

Geometrical linear responses and directional energy derivatives for energetically degenerate MCSCF electronic functions

For state-averaged multiconfigurational self consistent field (SA-MCSCF) wave functions, second-order geometrical response equations are derived that allow the determination of first-order configuration amplitude response for equally weighted, energetically degenerate states. The first-order response equations obtained in earlier work do not suffice to determine these particular responses parameters. To formulate such a derivation in a well defined manner, it is found that a specific linear combination of the degenerate states must be formed; this specific combination of states then defines how state energies and wave functions evolve as one passes through the surface intersection. The linear combination among the degenerate states is dependent upon the molecular distortion for which the responses are to be evaluated. Expressions for first- and second-order directional energy derivatives for these energetically degenerate wave functions are also derived. All the equations obtained are computationally tractable and expressed in terms of quantities that result from optimizing the SA-MCSCF wave functions and from solving the first- and part of the second-order geometrical response equations.

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

AbstractThe 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.

Spectroscopic properties of 34 electronic states of zirconium dimer (Zr2)

State-averaged complete active space multiconfiguration self-consistent field followed by multireference singles + doubles configuration interaction calculations are carried out on low-lying electronic states of zirconium dimer (Zr2). In addition relativistic configuration interaction calculations are carried out including spin–orbit effects. Thirty-four bound electronic states are found for Zr2. Three very low-lying states of 7∑+u, 3∑+u, and 1∑+g symmetries are found as candidates for the ground state. Higher-order correlation effects and extension of basis sets tend to favor the 1∑+g state as the ground state of Zr2 exhibiting approximately a quadruple bond (bond order =3.6). Complete potential energy curves of seven states of Zr2 are presented. The nature of low-lying electronic states is analyzed through Mulliken populations, natural orbitals and their occupations, spin–orbit effects and weights of various configurations.

On the Mg(3P)–He(1S) interaction using SA-MCSCF/ICF-CI wave functions

State averaged-multiconfiguration self-consistent-field (SA-MCSCF)/interacting correlated fragment-configuration interaction (ICF-CI) wave functions developed from an extended basis of Slater type orbitals are used to determine the portion of the nonrelativistic Born–Oppenheimer 3Σ+ and 3Π potential energy curves (PEC’s), relevant to fine structure changing collisions in the system Mg(3P)-He(1S). Using the finite perturbation method the parallel and perpendicular polarizabilities of Mg(3P) at the SA-MCSCF level are found to be α∥ =120 a.u.3 and α⊥ =84.5 a.u.3 The PEC’s exhibit the requisite (weak) long-range attraction, with E(3Σ+)<E(3Π) initially, in agreement with α∥>α⊥. The 3Σ+ and 3Π curves, which are rigorously degenerate at R(Mg–He)=∞, cross near R(Mg–He)=14 a.u. The 3Σ+ curve exhibits a very shallow minimum (∼1.5 cm−1) near R(Mg–He)=13.7 a.u. while a deeper minimum ∼16 cm−1 is found for the 3Π curve near R(Mg–He)=7.9 a.u. The effects of spin-orbit coupling are incorporated in a semiempirical manner. The SA-MCSCF/ICF-CI approach is compared with the results of a more standard MCSCF/ICF-CI treatment.

On the electronic structure of the X, A, and B states of CaCl

State-averaged multiconfiguration self-consistent-field (SA-MCSCF)/configuration interaction wave functions are used to characterize the near equilibrium electronic structure of the X 2Σ+, A 2Π, and B 2Σ+ states of CaCl. Spectroscopic constants Te, ωe, and Re were determined and are in reasonable agreement with experiment although the Re are uniformly long. The dipole moments for the X, A, and B states and the electronic transition moments for the A–X, B–X, and B–A systems were determined at the CI level and are in good agreement with the available experimental data. The three states are described by a Ca+2Cl− core plus one electron in a nonbonding calcium centered orbital, which is polarized away from the Cl− ion. The present calculations are in general accord with the polarizable ion model which has been inferred from experimental analyses of these states. However, participation of the calcium 3d orbital in the A 2Π state is surprisingly limited. Calculations in which the chlorine K and L shells are replaced by effective core potentials reproduce the results of the all electron calculations quite well.

Radiative lifetimes and transition moments in MgO

An experimental and theoretical study of several transitions in the MgO molecule is reported. The radiative lifetime of the MgO B 1Σ + v'=0 level is measured to be 32.7±1.7 nsec, while that of the electronic state(s) excited by 372 nm radiation ( d 3Δ and/or f 3Π) is 11.8±0.5 nsec. The B-X and A-X transition moments are calculated using state averaged multiconfiguration self-consistent field and configuration interaction methods. With an estimate of the B-A transition moment derived from an earlier calculation, the radiative lifetime of the B 1Σ + v'=0 level is computed to be 24 nsec. A value of 0.23 msec is calculated for the lifetime of A 1Π v'=0.

The electronic structure of CaO. II. An MCSCF/CI treatment of the low-lying 1Σ+ and 1Π states

State averaged multiconfiguration self-consistent field and configuration interaction methods are used to discuss the 1,2 1Σ+ states of CaO. Spectroscopic constants Re, Te, and ωe are determined. In addition, radiative transitions between the 1,2 1Σ+ states, and the 1 1Π states are discussed. The spectroscopic constants are in reasonable agreement with experiment although the predicted bond lengths are uniformly long. The calculated lifetime for the v=6 level of the A 1Σ+ state of 130×10−9 s is in good agreement with a preliminary experimental value. The lifetime of low-lying vibrational states in the A′ 1Π manifold are over an order of magnitude longer than their A state counterparts. The v=0 level of the A′ 1Π state is predicted to have a lifetime of 25×10−6 s.