A new theoretical approach to two-photon transition intensities at the multiconfigurational self-consistent field (MCSCF) level of theory, is described in detail. The fundamental property of an MCSCF wave function, that it is possible to define the response equations for an excited state, is a prerequisite. The method requires solely first-order multiconfigurational response calculations, because the equations involve the response of both the initial and final state. However, the method is approximate as the coupling between the +ω and −ω parts of the linear response is disregarded. The complete active space state interaction (CASSI) method is applied in the evaluation of the involved matrix elements. To illustrate the performance and the requirements of this method, it was used to determine TP transitions in trans-1,3-butadiene and trans-stilbene.

An efficient method for calculating the Lagrange multipliers and the analytical gradients of one state included in a state average MCSCF wave function is presented. It is demonstrated that the state average energy of an ‘equal-weight’ scheme is invariant to rotations within the state average subspace and that the corresponding rotations should be eliminated from the Lagrangian equations. Finally, a diagnostic is presented, which gauges the energy difference between a state defined by a state average calculation and the corresponding fully variational multi-configurational SCF state.

We present a theoretical study on the dissociation reaction of N8 azapantalene to four N2 molecules. The process proceeds via isomerization of N8 azapentalene to N8 azidopentazole, which then dissociates directly into four nitrogen molecules. The calculations have determined the relative energies of the two isomers and the two transition states involved in the dissociation process. The results show azidopentazole to be 13 kcal/mol more stable than azapentalene. The barrier to dissociation into four N2 molecules is computed to be 19 kcal/mol. It is concluded that N8 is not stable enough to be considered as a candidate for a high-energy density material. The calculations have been carried out using multiconfigurational self-consistent field and second-order perturbation theory. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 311–315, 2000

The two lowest bands, B2u and B1u , of the electronic spectrum of the benzene molecule have been studied theoretically using a new method to compute vibronic excitation energies and intensities. The complete active space ~CAS! self-contained field~SCF! method~with six active p-orbitals! was used to compute harmonic force field for the ground state and the B2u and B1u electronic states. A linear approximation has been used for the transition dipole as a function of the nuclear displacement coordinates. Derivatives of the transition dipole were computed using a variant of the CASSCF state interaction method. Multiconfigurational second-order perturbation theory ~CASPT2! was used to obtain absolute excitation energies ~12 activep-orbitals!. The results show that the approach works well. Vibrational progressions are well described in both bands and intensities, and energies are in agreement with experiment, in particular when CASPT2 derived geometries are used. One interesting result is that computed vertical energies fall about 0.1 eV on the high energy side of the band maximum. © 2000 American Institute of Physics. @S0021-9606 ~00!30306-3#

The C3H2 isomers are important molecules in interstellar space. An understanding of their electronic structure can contribute significantly to the interpretation of interstellar spectra. In a theoretical study of the C3H2 isomers a multiconfigurational treatment is of interest because many of the isomers are carbenes or diradicals. We present such an investigation of all possible C3H2 isomers. The most important features of their electronic and vibrational spectra are calculated. Earlier theoretical studies are reviewed and it is shown that the present study yields the same order of stability for the singlet and triplet states as most previous studies.

The two lowest bands, B-1(2u) and B-1(1u), of the electronic spectrum of the benzene molecule have been studied theoretically using a new method to compute vibronic excitation energies and intensities. The complete active space (CAS) self-contained field (SCF) method (with six active pi-orbitals) was used to compute harmonic force field for the ground state and the B-1(2u) and B-1(1u) electronic states. A linear approximation has been used for the transition dipole as a function of the nuclear displacement coordinates. Derivatives of the transition dipole were computed using a variant of the CASSCF state interaction method. Multiconfigurational second-order perturbation theory (CASPT2) was used to obtain absolute excitation energies (12 active pi-orbitals). The results show that the approach works well. Vibrational progressions are well described in both bands and intensities, and energies are in agreement with experiment, in particular when CASPT2 derived geometries are used. One interesting result is that computed vertical energies fall about 0.1 eV on the high energy side of the band maximum. (C) 2000 American Institute of Physics. [S0021-9606(00)30306-3].

The two lowest bands, 1B2u and 1B1u, of the electronic spectrum of the benzene molecule have been studied theoretically using a new method to compute vibronic excitation energies and intensities. The complete active space (CAS) self-contained field (SCF) method (with six active π-orbitals) was used to compute harmonic force field for the ground state and the 1B2u and 1B1u electronic states. A linear approximation has been used for the transition dipole as a function of the nuclear displacement coordinates. Derivatives of the transition dipole were computed using a variant of the CASSCF state interaction method. Multiconfigurational second-order perturbation theory (CASPT2) was used to obtain absolute excitation energies (12 active π-orbitals). The results show that the approach works well. Vibrational progressions are well described in both bands and intensities, and energies are in agreement with experiment, in particular when CASPT2 derived geometries are used. One interesting result is that computed vertical energies fall about 0.1 eV on the high energy side of the band maximum.

The thermochemistry of the benzynes has been reinvestigated in a set of benchmark calculations including, e.g., multireference perturbation theory in combination with large basis sets up to correlation consistent polarized valence quadruple xi followed by basis set extrapolation procedures. The vibrational corrections have been deduced from multiconfiguration self-consistent field (MCSCF) calculations employing average atomic natural orbital basis sets. The quality of the isodesmic reactions has been investigated by analyzing the errors of the utilized methods in predicting the CH bond strengths and energies of the related molecules. It turns out that multireference third order perturbation theory, although occasionally better than second order, suffers from less systematic errors and thus is not as well suited for use in isodesmic reactions as the corresponding second order theory. The present extended calculations show that all the isodesmic reactions used in previous studies of the thermochemistry of the benzynes are adequate. Furthermore, it is demonstrated that multireference second order perturbation theory accurately reproduces the singlet-triplet energy splittings of the benzynes.

A direct implementation of the reduced multiplication scheme of the Rys—Gauss quadrature in the computation of the second-order geometric derivatives for MCSCF wavefunctions is presented. Characteristics unique to this implementation are simultaneous evaluation of first- and second-order two-electron integral derivatives, compact representation of intermediate elements and efficient prescreening. Finally, a novel technique for the preconditioning of the response equations is reported. Applications sizing up to 510 basis functions are included in the presentation.

HOOClO2 was produced by addition of hydrogen atoms to a mixture of O-2 and OClO on the surface of growing argon matrixes at 17 K. The compound was identified by infrared spectroscopy utilizing the H to D and O-18(2) and O-16,18(2) spectral shifts. The matrices were irradiated with the full radiation from a 300-W Xe lamp. HOOClO2 was eliminated by the irradiation, but we were unable to identify the photodecomposition product. Ab initio calculations show that HOO binds to OClO with a bond strength intermediate between a van der Waals interaction and a covalent bond.

A novel procedure to select internal coordinates for molecular geometry optimizations is presented. The procedure has features in common with other so-called redundant internal coordinates schemes. It is a black-box method which automatically selects an appropriate set of internal coordinates in which the geometry optimization is performed. The method is explicitly expressed in the non-redundant parameter space, thus avoiding the need for projections from the redundant internal coordinate space. The new procedure introduces a weighting in which the redundancy is modified prior to the generation of the non-redundant internal coordinates. The new method favors those redundant internal coordinates which are the most significant. It has favorable properties for the automatic generation of molecular coordinates in van der Waals complexes and transition state optimizations.

The properties of methylene peroxide in the gas phase and water have been examined. The solution effects have been modeled with a cavity. To make it possible to optimize the geometry of the cavity, we have added an approximate description of the Pauli repulsion between the solvent and the solute. An efficient direct implementation of the calculation of multicenter multipole operators is also described. We have applied the method to calculate the electric properties of methylene peroxide, a system that is characterized by its near degeneracy between a biradical and a zwitterionic state. As expected, it is shown that solvent effects will stabilize the ionic configuration, resulting in a considerably weakened OO bond and an increased double bond character in the CO bond. The theoretical study has been performed using the multiconfigurational (CAS) SCF method and second-order perturbation theory (CASPT2).

When a molecular equilibrium geometry is determined by minimizing the energy by a quasi-Newton-Raphson method, the number of iterations required depends critically on the choice of an approximate molecular Hessian matrix. We find that a simple 15-parameter function of the nuclear positions gives a good choice for any molecule with atoms from the first three rows of the periodic table. This Hessian is used for ab initio geometry optimizations with the quasi-Newton-Raphson method, with or without update. The equilibrium geometries of 30 molecules, with a variety of sizes and symmetries, is obtained with the new scheme, which is shown to converge significantly faster than other methods.

The autoaromatization of (Z)-hex-3-ene-1,5-diyne to the singlet biradical p-benzyne has been reinvestigated by state of the art ab initio methods. Previous CCSD(T)/6-31G(d,p) and CASPT2[0]/ANO[C(5s4p2dlf)/H(3s2p)] calculations estimated the reaction heat at 298 K to be 8-10 and 3.9 +/- 3.2 kcal/mol, respectively. Recent NO- and oxygen-dependent trapping experiments and collision-induced dissociation threshold energy experiments estimate the heat of reaction to be 8.5 +/- 1.0 kcal/mol at 470 K (corrected to 9.5 +/- 1.0 kcal/mol at 298 K) and 8.4 +/- 3.0 kcal/mol at 298 K, respectively. New theoretical estimates at 298 K predict the values at the basis set Limit for the CCSD(T) and CASPT2[gl] methods to be 12.7 +/- 2.0 and 5.4 +/- 2.0 kcal/mol, respectively. The experimentally predicted electronic contribution to the heat of activation is 28.6 kcal/mol. This can be compared with 25.5 and 29.8 kcal/mol from the CASPT2[gl] and the CCSD(T) methods, respectively. The new study has a much larger one-particle basis set for the CCSD(T) method as compared to earlier studies. For the CASPT2 investigation the better suited CASPT2[gl] approximation is utilized. The original CASPT2 method, CASPT2[0], systematically favors open-shell systems relative to closed-shell systems. This was previously corrected empirically. The current study shows that the energy difference between CCSD(T) and CASPT2[gl] at the basis set limit is estimated to be 7 +/- 2 kcal/mol. The study also demonstrates that the estimated heat of reaction is very sensitive to the quality of the basis set. In particular CCSD(T)/6-31G(d,p) approach underestimates the basis set limit of the enthalpy by approximately 5 kcal/mol. Furthermore, the relative energies of the p-, m-, and o-benzynes are computed at the CASPT2[gl] and CCSD(T) levels of theory. These results help to explain the discrepancy between the two methods in the case of the Bergman reaction. The deficiency of the CASPT2 method is mainly attributed to the approximate way in which the dynamic correlation is included by perturbation theory. A similar sized error is attributed to the CCSD(T) method due to the approximate way in which near degeneracy effects are included. This combined CCSD(T) and CASPT2[gl] study indicates that the most recent experimental value of the p-benzyne-o-benzyne energy splitting is overestimated.