Complete Active Space Valence Bond Research Articles

Canonical-ensemble state-averaged complete active space self-consistent field (SA-CASSCF) strategy for problems with more diabatic than adiabatic states: charge-bond resonance in monomethine cyanines.

This paper reviews basic results from a theory of the a priori classical probabilities (weights) in state-averaged complete active space self-consistent field (SA-CASSCF) models. It addresses how the classical probabilities limit the invariance of the self-consistency condition to transformations of the complete active space configuration interaction (CAS-CI) problem. Such transformations are of interest for choosing representations of the SA-CASSCF solution that are diabatic with respect to some interaction. I achieve the known result that a SA-CASSCF can be self-consistently transformed only within degenerate subspaces of the CAS-CI ensemble density matrix. For uniformly distributed ("microcanonical") SA-CASSCF ensembles, self-consistency is invariant to any unitary CAS-CI transformation that acts locally on the ensemble support. Most SA-CASSCF applications in current literature are microcanonical. A problem with microcanonical SA-CASSCF models for problems with "more diabatic than adiabatic" states is described. The problem is that not all diabatic energies and couplings are self-consistently resolvable. A canonical-ensemble SA-CASSCF strategy is proposed to solve the problem. For canonical-ensemble SA-CASSCF, the equilibrated ensemble is a Boltzmann density matrix parametrized by its own CAS-CI Hamiltonian and a Lagrange multiplier acting as an inverse "temperature," unrelated to the physical temperature. Like the convergence criterion for microcanonical-ensemble SA-CASSCF, the equilibration condition for canonical-ensemble SA-CASSCF is invariant to transformations that act locally on the ensemble CAS-CI density matrix. The advantage of a canonical-ensemble description is that more adiabatic states can be included in the support of the ensemble without running into convergence problems. The constraint on the dimensionality of the problem is relieved by the introduction of an energy constraint. The method is illustrated with a complete active space valence-bond (CASVB) analysis of the charge/bond resonance electronic structure of a monomethine cyanine: Michler's hydrol blue. The diabatic CASVB representation is shown to vary weakly for "temperatures" corresponding to visible photon energies. Canonical-ensemble SA-CASSCF enables the resolution of energies and couplings for all covalent and ionic CASVB structures contributing to the SA-CASSCF ensemble. The CASVB solution describes resonance of charge- and bond-localized electronic structures interacting via bridge resonance superexchange. The resonance couplings can be separated into channels associated with either covalent charge delocalization or chemical bonding interactions, with the latter significantly stronger than the former.

An efficient algorithm for complete active space valence bond self-consistent field calculation

This article describes a novel algorithm for the optimization of valence bond self-consistent field (VBSCF) wave function for a complete active space (CAS), so-called VBSCF(CAS). This was achieved by applying the strategies adopted in the optimization of CASSCF wave functions to VBSCF(CAS) wave functions, using an auxiliary orthogonal orbital set that generates the same configuration space as the original nonorthogonal orbital set. Theoretical analyses and test calculations show that the VBSCF(CAS) method shares the same computational scaling as CASSCF. The test calculations show the current capability of VBSCF method, which involves millions of VB structures.

Electronic structures of low-lying Bu excited states in trans-oligoenes: Pariser-Parr-Pople and ab initio calculations

Two lowest-lying excited singlets with B(u) symmetry of all-trans-oligoenes, the well-known ionic 1(1)B(u)(+) state as well as the "hidden" ionic-covalent-mixed 1(1)B(u)(-) state, are calculated within both the Pariser-Parr-Pople (PPP) model at full configuration interaction (FCI) level and ab initio methods. The vertical excitation energies as well as wavefunctions from PPP-FCI calculations are found to be in good agreement with those from high-level multi-reference methods, such as multi-reference complete active space self-consistent field (CASSCF) with second order perturbative corrections (CASPT2), multi-reference Møller-Plesset perturbation theory (MRMP), and complete active space valence bond theory (CASVB). The oscillator strengths from PPP calculation are in good agreement with spectroscopy experiments. The relatively small oscillator strength of 1(1)B(u)(-) is due to the approximate electron-hole symmetry of this state. In addition, the bond lengths in both states are found to show remarkable relativity with the bond orders calculated with ground state geometries, which suggests a possible strategy for initial guess in geometry optimization of excited states.

On the Stability, Electronic Structure, and Nonlinear Optical Properties of HXeOXeF and FXeOXeF

The electronic ground state, stability, and linear and nonlinear optical properties of HXeOXeF and FXeOXeF have been studied theoretically by employing complete active space valence bond (CASVB), multistate complete active space perturbation theory (MS-CASPT2), and coupled cluster methods. It is shown that the oxygen inserted between the two Xe atoms significantly modifies the ground-state electronic configuration of the formed derivative by increasing the closed-shell contribution (σ(2)) and removing the diradicaloid character observed in HXe(2)F. The electronic charge distribution has been analyzed by employing the atoms-in-molecules (AIM) method. The dissociation channels of HXeOXeF and FXeOXeF have been studied in detail. It was found that these compounds are metastable, protected by substantial energy barriers and, thus, they can be prepared under appropriate conditions. Both two- and three-body dissociation reactions have been considered. The effects of inserting O in HXe(2)F and substituting H (HXeOXeF) by F, leading to FXeOXeF, on the energy barriers are discussed. The significant effects of the inserted oxygen on the polarizability and even more on the first hyperpolarizability have been computed and rationalized.

On the Electronic Structure of H-Ng-Ng-F (Ng = Ar, Kr, Xe) and the Nonlinear Optical Properties of HXe2F.

The electronic ground state of H-Ng-Ng-F (Ng = Ar, Kr, Xe) has been studied theoretically by employing the ab initio complete active space valence bond (CASVB) and multi-state complete active space perturbation theory (MS-CASPT2) methods. Both levels of theory confirm the diradicaloid character (DC) of the HNg2F ground state, increasing in the order Ar > Kr > Xe. The very significant effect of the first and, even more, the second Xe atom on the (hyper)polarizabilities has been shown and interpreted. Thus, the present results demonstrate a mechanism for producing very large (hyper)polarizabilities.

Valence-bond description of chemical reactions on Born–Oppenheimer molecular dynamics trajectories

The nature of chemical bonds on dynamic paths was investigated using the complete active space valence-bond (CASVB) method and the Born-Oppenheimer dynamics. To extract the chemical bond picture during reactions, a scheme to collect contributions from several VB (resonance) structures into a small numbers of indices was introduced. In this scheme, a tree diagram for the VB structures is constructed with the numbers of the ionic bonds treated as generation. A pair of VB structures is related to each other if one VB structure is transferred into the other by changing a covalent bond to an ionic bond. The former and latter VB structures are named parent and child structures, respectively. The weights of the bond pictures are computed as the sum of the CASVB occupation numbers running from the top generation to the bottom along the descent of the VB structures. Thus, a number of CASVB occupation numbers are collected into a small number of indices, and a clear bond picture may be obtained from the CASVB wave function. The scheme was applied to the hydrogen exchange reaction H(2)+F-->H+HF and the Diels-Alder reaction C(5)H(6)(cyclopentadiene)+CH(2)=CH(2)(ethylene)-->C(7)H(10)(norbornene). In both the reactions, the scheme gave a clear picture for the Born-Oppenheimer dynamics trajectories. The reconstruction of the bonds during reactions was well described by following the temporal changes in weight.

Linear and nonlinear optical properties of some organoxenon derivatives

We employ a series of state-of-the-art computational techniques to study the effect of inserting one or more Xe atoms in HC2H and HC4H, on the linear and nonlinear optical (L&NLO) properties of the resulting compounds. It has been found that the inserted Xe has a great effect on the L&NLO properties of the organoxenon derivatives. We analyze the bonding in HXeC2H, and the change of the electronic structure, which is induced by inserting Xe, in order to rationalize the observed extraordinary L&NLO properties. The derivatives, which are of interest in this work, have been synthesized in a Xe matrix. Thus the effect of the local field (LF), due to the Xe environment, on the properties of HXeC2H, has also been computed. It has been found that the LF effect on some properties is significant. The calculations have been performed by employing a hierarchy of basis sets and the techniques MP2 and CCSD(T) for taking into account correlation. For the interpretation of the results we have employed the complete active space valence bond and CASSCF/CASPT2 methods.

Complete active space valence bond method applied to chemical reactions

A complete active space valence bond (CASVB) method with orthogonal and non-orthogonal orbitals is applied to the collinear exchange reaction H+H 2→H 2+H and the unimolecular dissociation H 2CO→H 2+CO. The bond nature during the reactions is analyzed using the occupation number (weight) of the valence bond resonance structures. The CASVB descriptions with orthogonal and non-orthogonal orbitals give a similar picture, although the ratio of covalent vs. ionic bonds are quite different. In the H 2CO→H 2+CO reaction, the CH bond dissociation and HH bond formation occur after passing through the transition state. CASVB gives a clear understanding of reaction mechanisms in terms of competing bonding schemes whose weights change along the intrinsic reaction coordinate.

A complete active space valence bond method with nonorthogonal orbitals

A complete active space self-consistent field (SCF) wave function is transformed into a valence bond type representation built from nonorthogonal orbitals, each strongly localized on a single atom. Nonorthogonal complete active space SCF orbitals are constructed by Ruedenberg’s projected localization procedure so that they have maximal overlaps with the corresponding minimum basis set of atomic orbitals of the free-atoms. The valence bond structures which are composed of such nonorthogonal quasiatomic orbitals constitute the wave function closest to the concept of the oldest and most simple valence bond method. The method is applied to benzene, butadiene, hydrogen, and methane molecules and compared to the previously proposed complete active space valence bond approach with orthogonal orbitals. The results demonstrate the validity of the method as a powerful tool for describing the electronic structure of various molecules.

A complete active space valence bond (CASVB) method

A complete active space valence bond (CASVB) method is proposed which is particularly adapted to chemical interpretation. A CASVB wave function can be obtained simply by transforming a canonical CASSCF function and readily interpreted in terms of the well known classical VB resonance structures. The method is applied to the ground and excited states of benzene, butadiene, and the ground state of methane. The CASVB affords a clear view of the wave functions for the various states. The electronic excitation is represented in a VB picture as rearrangements of the spin couplings or as charge transfers which involve breaking covalent bonds and forming new ionic bonds. The former gives rise to covalent excited states and the latter to ionic excited states. The physical reasons why it is so difficult to describe the ionic excited states at the CASSCF level with a single active space and why the lowest 1 1B+2 state in cis-butadiene is so stabilized compared to the corresponding 1 1B+u state in the trans isomer are easily identified in view of a VB picture. The CASVB forms a useful bridge from molecular orbital theory to the familiar concepts of chemists.