[Show abstract][Hide abstract] ABSTRACT: The electronic structures of oxides of selenium, SeO, SeO2, and SeO3, and their dimers, Se2O3 and Se2O5, were studied using the second-order Generalised van Vleck variant of multireference perturbation theory (GVVPT2), with comparison to the linked completely renormalised coupled cluster through perturbative triple excitations, i.e., CR-CC(2,3), theory. Geometry optimisations of SeO, SeO2, and SeO3 using GVVPT2 and the cc-pVTZ basis set show close agreement with CR-CC(2,3) results and, for SeO and SeO2, close agreement with experiment. In contrast, both GVVPT2 and CR-CC(2,3) predict that the re bond length of SeO3 is significantly shorter (ca. 0.1 A°) than the r0 experimental value. Calculations of energies of oxidation reactions predict the formation of SeO2 and SeO3 from SeO to be exothermic. The geometries and energetics of four isomers of both Se2O3 and Se2O5 have been characterised using a composite methodology; key transition states between the isomers were similarly calculated. Because of comparable energies, and relatively low transition barrier heights, several isomers of the dimeric species are predicted to be chemically relevant. Harmonic vibrational frequencies of monomeric and dimeric selenium oxides were obtained at the B3LYP/6-311G∗ level of theory and corroborate geometrical data that many of the characteristics of the monomeric selenium oxides are preserved in the dimeric species.
[Show abstract][Hide abstract] ABSTRACT: The diatomic carbon molecule has a complex electronic structure with a large number of low-lying electronic excited states. In this work, the potential energy curves (PECs) of the four lowest lying singlet states (
$X^{1} \Sigma^{ + }_{g}$
,
$A^{1} \Pi_{u}$
,
$B^{1} \Delta_{g}$
, and
$B^{\prime1} \Sigma^{ + }_{g}$
) were obtained by high-level ab initio calculations. Valence electron correlation was accounted for by the correlation energy extrapolation by intrinsic scaling (CEEIS) method. Additional corrections to the PECs included core–valence correlation and relativistic effects. Spin–orbit corrections were found to be insignificant. The impact of using dynamically weighted reference wave functions in conjunction with CEEIS was examined and found to give indistinguishable results from the even weighted method. The PECs showed multiple curve crossings due to the
$B^{1} \Delta_{g}$
state as well as an avoided crossing between the two
$^{1} \Sigma^{ + }_{g}$
states. Vibrational energy levels were computed for each of the four electronic states, as well as rotational constants and spectroscopic parameters. Comparison between the theoretical and experimental results showed excellent agreement overall. Equilibrium bond distances are reproduced to within 0.05 %. The dissociation energies of the states agree with experiment to within ~0.5 kcal/mol, achieving “chemical accuracy.” Vibrational energy levels show average deviations of ~20 cm−1 or less. The
$B^{1} \Delta_{g}$
state shows the best agreement with a mean absolute deviation of 2.41 cm−1. Calculated rotational constants exhibit very good agreement with experiment, as do the spectroscopic constants.
[Show abstract][Hide abstract] ABSTRACT: A Lagrangian based approach was used to obtain analytic formulas for nonadiabatic coupling terms within a multireference perturbation theory description of molecular electronic structure. Specifically, formulas were developed for the second-order generalized Van Vleck perturbation theory (GVVPT2) description of electron correlation. The formalism can use either complete or incomplete model (or reference) spaces, and is limited, in this regard, only by the capabilities of the MCSCF program. Of particular interest, the suggested formalism can straightforwardly use state-averaged MCSCF descriptions of the reference space in which the states have arbitrary weights. Since GVVPT2 wave functions are not strictly orthogonal, the definition of nonadiabatic coupling terms is untrivial and a perturbation-order consistent definition is suggested herein from which working equations are developed.
Chemical Physics 06/2012; DOI:10.1016/j.chemphys.2011.09.014 · 1.65 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: With relatively simple model spaces derived from valence bond models, a straightforward zero-order Hamiltonian, and the use of moderate-sized Dunning-type correlation consistent basis sets (cc-pVTZ, aug-cc-pVTZ, and cc-pVQZ), the second order generalized Van Vleck perturbation theory (GVVPT2) method is shown to produce potential energy curves (PECs) and spectroscopic constants close to experimental results for both ground and low-lying excited electronic states of Sc(2), Cr(2) and Mn(2). In spite of multiple quasidegeneracies (particularly for the cases of Sc(2) and Mn(2)), the GVVPT2 PECs are smooth with no discontinuities. Since these molecules have been identified as ones that widely used perturbative methods are inadequate for describing well, due to intruder state problems, unless shift parameters are introduced that can obfuscate the physics, this study suggests that the conclusion about the inadequacy of multireference perturbation theory be re-evaluated. The ground state of Sc(2) is predicted to be X(5)∑(u)(-), and its spectroscopic constants are close to the ones at the MRCISD level. Near equilibrium geometries, the 1(3)∑(u)(-) electronic state of Sc(2) is found to be less stable than the quintet ground state by 0.23 eV. The Cr(2) PEC has several features of the Rydberg-Klein-Rees (RKR) experimental curve (e.g., the pronounced shelf at elongated bond lengths), although the predicted bond length is slightly long (R(e) = 1.80 Å with cc-pVQZ compared to the experimental value of 1.68 Å). The X(1)∑(g)(+) ground state of Mn(2) is predicted to be a van der Waals molecule with a long bond length, R(e), of 3.83 Å using a cc-pVQZ basis set (experimental value = 3.40 Å) and a binding energy, D(e), of only 0.05 eV (experimental value = 0.1 eV). We obtained R(e) = 3.40 Å and D(e) = 0.09 eV at the complete basis set (CBS) limit for ground state Mn(2). Low lying excited state curves have also been characterized for all three cases (Cr(2), Mn(2), and Sc(2)) and show similar mathematical robustness as the ground states. These results suggest that the GVVPT2 multireference perturbation theory method is more broadly applicable than previously documented.
The Journal of Physical Chemistry A 04/2012; 116(18):4590-601. DOI:10.1021/jp300401u · 2.69 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A Lagrangian based approach was used to obtain analytic formulas for GVVPT2 energy nuclear gradients. The formalism can use either complete or incomplete model (or reference) spaces, and is limited, in this regard, only by the capabilities of the MCSCF program. An efficient means of evaluating the gradient equations is described. Demonstrative calculations were performed and compared with finite difference calculations on several molecules and show that the GVVPT2 gradients are accurate. Of particular interest, the suggested formalism can straightforwardly use state-averaged MCSCF descriptions of the reference space in which the states have arbitrary weights. This capability is demonstrated by some calculations on the ground and first excited singlet states of LiH, including calculations near an avoided crossing. The accuracy and usefulness of the GVVPT2 method and its gradient are highlighted by comparing the geometry of the near-C(2v) minimum on the conical intersection seam between the 1 (1)A(1) and 2 (1)A(1) surfaces of O(3) with values that were calculated at the multireference configuration interaction, including single and double excitations (MRCISD), level of theory.
The Journal of Chemical Physics 07/2011; 135(4):044117. DOI:10.1063/1.3611049 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A new formulation for multireference configuration interaction method, with single and double excitations (MRCISD), energy gradients and nonadiabatic coupling terms based on a Lagrangian approach is suggested and the gradients demonstrated to be accurate with calculations on several molecules. Of particular interest, the suggested formalism can straightforwardly use state-averaged-multiconfiguration self-consistent field (SA-MCSCF) descriptions of the reference space in which the states have arbitrary weights. This capability is demonstrated by some calculations on the ground and first excited 1Σ+ states of LiH, including calculations near an avoided crossing. The formalism can use either complete or incomplete model (i.e. reference) spaces, and is limited, in this regard, only by the capabilities of the MCSCF program. The formalism for nonadiabatic coupling shares many structural features with the energy gradient formalism, with the use of a function that corresponds to the energy for the coupling.
[Show abstract][Hide abstract] ABSTRACT: A Lagrangian approach for electric dipoles within second order Generalized Van Vleck Perturbation Theory (GVVPT2) is presented. The Lagrangian approach for this response property requires that only one, perturbation-independent, set of simultaneous equations needs to be solved. The presented formulation is demonstrated numerically on several well studied molecules at their equilibrium bond lengths and on the complete potential energy curves of the ground and first excited states of LiH. Numerical corroboration of the expected continuity for molecular properties for the GVVPT2 method is observed. It is seen that the GVVPT2 electric dipoles are in good agreement with experiment and with other high accuracy theoretical methods.
Chemical Physics Letters 02/2010; 487(1):116-121. DOI:10.1016/j.cplett.2010.01.003 · 1.90 Impact Factor