Potential energy curve for isomerization of N2H2 and C2H4 using the improved virtual orbital multireference Møller-Plesset perturbation theory

Multireference M?ller-Plesset (MRMP) perturbation theory [K. Hirao, Chem. Phys. Lett. 190, 374 (1992)] is modified to use improved virtual orbitals (IVOs) and is applied to study ground state potential energy curves for isomerization and dissociation of the N2H2 and C2H4 molecules. In contrast to traditional MRMP or multistate multiconfiguration quasidegenerate perturbation theory where the reference functions are obtained from (often difficult to converge) state averaged multiconfiguration self-consistent field methods, our reference functions are represented in terms of computationally efficient IVOs. For convenience in comparisons with other methods, a first order complete active space configuration interaction (CASCI) calculation with the IVOs is followed by the use of the IVOs in MRMP to incorporate residual electron correlation effects. The potential energy curves calculated from the IVO-MRMP method are compared with computations using state-of-the-art coupled cluster singles and doubles (CCSD) methods and variants thereof to assess the efficacy of the IVO-MRMP scheme. The present study clearly demonstrates that unlike the CCSD and its variants, the IVO-MRMP approach provides smooth and reliable ground state potential energy curves for isomerization of these systems. Although the rigorously size-extensive completely renormalized CC theory with noniterative triples corrections (CR-CC(2,3)) likewise provides relatively smooth curves, the CR-CC(2,3) calculations overestimate the cis-trans barrier height for N2H2. The ground state spectroscopic constants predicted by the IVO-CASCI method agree well with experiment and with other highly correlated ab initio methods.     

Fixed-node diffusion Monte Carlo study of the structures of m-benzyne

Diffusion Monte Carlo (DMC) calculations are performed on the monocyclic and bicyclic forms of m-benzyne, which are the equilibrium structures at the CCSD(T) and CCSD levels of coupled cluster theory. We employed multiconfiguration self-consistent field trial wave functions which are constructed from a carefully selected eight-electrons-in-eight-orbitals complete active space [CAS(8,8)], with configuration state function coefficients that are reoptimized in the presence of a Jastrow factor. The DMC calculations show that the monocyclic structure is lower in energy than the bicyclic structure by 1.9(2) kcal/mole, which is in excellent agreement with the best coupled cluster results.     

Dynamically weighted multiconfiguration self-consistent field: multistate calculations for F+H2O-->HF+OH reaction paths

A novel method of dynamically adjusted weighting factors in state-averaged multiconfiguration self-consistent-field calculations (SA-MCSCF) is described that is applicable to systems of arbitrary dimensionality. The proposed dynamically weighted approach automatically weights the relevant electronic states in each region of the potential energy surface, smoothly adjusting between these regions with an energy dependent functional. This method is tested on the F(2P)+H2O-->HF+OH(2Pi) reaction, which otherwise proves challenging to describe with traditional SA-MCSCF methods due to (i) different asymptotic degeneracies of reactant (threefold) and product (twofold) channels, and (ii) presence of low-lying charge transfer configurations near the transition state region. The smoothly varying wave functions obtained by dynamically weighted multiconfigurational self-consistent field represent excellent reference states for high-level multireference configuration interaction calculations and offer an ideal starting point for construction of multiple state potential energy surfaces.     

Polarization Green's function with multiconfiguration self-consistent-field reference states

The polarization Green's-function formalism in the superoperator notation of Goscinski and Lukman is re-derived using a multiconfiguration self-consistent-field (MC -SCF ) reference state to establish the superoperator metric. The potential advantages of employing this more general reference state in Green's-function theories and certain inherent weaknesses associated with the traditional Hartree–Fock or Rayleigh–Schrödinger perturbation theory reference state choices are briefly discussed. The Hermiticity of the superoperators is analyzed within the framework of the MC –SCF reference state. Using a concept of order appropriate for this reference state choice, explicit formulas and computational procedures for the implementation of this Green's-function theory are presented and specialized to include terms consistent through second order.     

Accurate Calculation of Equilibrium Reduced Density Matrix for the System-Bath Model: a Multilayer Multiconfiguration Time-Dependent Hartree Approach and its Comparison to a Multi-Electronic-State Path Integral Molecular Dynamics Approach?

An efficient and accurate method for computing the equilibrium reduced density matrix is presented for treating open quantum systems characterized by the system-bath model. The method employs the multilayer multiconfiguration time-dependent Hartree theory for imaginary time propagation and an importance sampling procedure for calculating the quantum mechanical trace. The method is applied to the spin-boson Hamiltonian, which leads to accurate results in agreement with those produced by the multi-electronic-state path integral molecular dynamics method.     

Multireference spin-adapted variant of density functional theory

A new Kohn-Sham formalism is developed for studying the lowest molecular electronic states of given space and spin symmetry whose densities are represented by weighted sums of several reference configurations. Unlike standard spin-density functional theory, the new formalism uses total spin conserving spin-density operators and spin-invariant density matrices so that the method is fully spin-adapted and solves the so-called spin-symmetry dilemma. The formalism permits the use of an arbitrary set of reference (noninteracting) configurations with any number of open shells. It is shown that the requirement of degeneracy of the total noninteracting energies of the reference configurations (or configuration state functions) is equivalent to the stationary condition of the exact energy relative to the weights of the configurations (or configuration state functions). Consequently, at any molecular geometry, the weights can be determined by minimization of the energy, and, for given reference weights, the Kohn-Sham orbitals can be determined. From this viewpoint, the developed theory can be interpreted as an analog of the multiconfiguration self-consistent field approach within density functional theory.     

Theoretical study of some bis-verdazyl diradicals: singlet–triplet energy gap

The bis-verdazyl diradical (BVD) system is closely examined by using the multiconfiguration wavefunctions as well as the density functional theory (DFT). The totally symmetric singlet ground state turns out to have strong multiconfiguration character at all levels of theory. The singlet ground state takes on the planar structure while the most stable triplet state corresponds to the twisted form. The MCSCF+MCQDPT2 calculations are shown to be sufficient to predict the singlet–triplet energy gap which is insensitive to the electronic characters of the ring substituents.     

Direct minimization of the energy functional in LCAO-MO density matrix formalism

The general multiconfiguration self-consistent-field method is presented along the density matrix formalism. The proposed optimization procedure for orbitals makes use of an orthogonal transformation in the space spanned by the fixed basis set. Acting on the unconstrained parameters of the transformation a direct minimization of the energy expression is performed using a gradient approach. A similar method may also be applied to the optimization of the expansion coefficients. The method works not only for the ground state of a given system, but also for any excited state, yielding an upper bound to the true energy of the considered state.     

Variational wavefunctions for low-lying excited states

The multiconfiguration method based on the generalized Brillouin theorem is well suited to optimize orbitals in variational wavefunctions for low-lying excited states of a given symmetry. Such wavefunctions are constrained to be orthogonal to and noninteracting with the wavefunctions for all lower states of the same symmetry. Test calculations were performed on the lowest excited ¹S state of Be. For a Hartree-Fock ground state wavefunction, singly excited configurations were insufficient to describe the lowest excited state, and triply excited configurations had to be added. For multiconfiguration ground state wavefunctions, however, singly excited configurations gave good results.     

Methods of composite molecular wave functions. I. Variational principle and multiconfiguration SCF theory

The Silverstone–Stuebing variational principle for the discontinuous wave functions of one-electron systems is generalized for many-electron systems. The variational functional of energy takes real or complex value. The condition that it is real is given. Using the generalized variational principle, a multiconfiguration SCF theory for the composite molecular wave function is formulated. According to the theory, we may divide the whole space into space-filling cells, solve the SCF equations in each cell and build up the wave functions of the system by gathering the wave functions obtained in the cells. For use in the basis-set expansion method, the SCF equations are rewritten as matrix forms in which only one- and two-center integrals appear if an expansion center is located in each cell.     

Multiconfiguration optimized effective potential method for a density-functional treatment of static correlation

An approach to treat static correlation within a density-functional framework is presented. To that end, a multiconfiguration optimized effective potential (MCOEP) method is derived. In contrast to standard multiconfiguration self-consistent field (MCSCF) methods and previous combinations of MCSCF procedures with density-functional theory, the MCOEP method yields well-defined physically meaningful orbital and eigenvalue spectra. In addition to the electronic ground state also excited electronic states can be described. The MCOEP method is implemented invoking the localized Hartree-Fock approximation, leading to a multiconfiguration localized Hartree-Fock approach. Applications of the new method to the dissociation of the hydrogen molecule and the isomerization of ethene and cyclobutadiene show that it is capable of describing situations that are characterized by strong static correlation.     

Numerically exact, time-dependent treatment of vibrationally coupled electron transport in single-molecule junctions

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory within second quantization representation of the Fock space, a novel numerically exact methodology to treat many-body quantum dynamics for systems containing identical particles, is applied to study the effect of vibrational motion on electron transport in a generic model for single-molecule junctions. The results demonstrate the importance of electronic-vibrational coupling for the transport characteristics. For situations where the energy of the bridge state is located close to the Fermi energy, the simulations show the time-dependent formation of a polaron state that results in a pronounced suppression of the current corresponding to the phenomenon of phonon blockade. We show that this phenomenon cannot be explained solely by the polaron shift of the energy but requires methods that incorporate the dynamical effect of the vibrations on the transport. The accurate results obtained with the ML-MCTDH in this parameter regime are compared to results of nonequilibrium Green's function theory.     

Block-correlated coupled cluster theory: the general formulation and its application to the antiferromagnetic Heisenberg model

The general formalism of the block-correlated coupled cluster (BCCC) method, an alternative multireference coupled cluster method for calculating the ground-state electronic structures of molecular systems, has been presented. The BCCC theory is constructed in terms of a complete set of many-electron states of individual blocks, assumed that the whole system could be partitioned into a set of blocks. The reference state in the BCCC is selected as a tensor product of the most important many-electron state of each system block. By truncating the cluster operator to a certain n-block correlation level, an approximate but size-extensive BCCC method, denoted as BCCCn, is defined. For reducing the computational effort but without much loss of accuracy, the reduced density matrix is introduced to generate an optimal subset of many-electron states for each block. I have implemented the BCCCn (n=2,3) methods within the S=1/2 Heisenberg Hamiltonian, and applied them to calculate the ground-state energies of one-dimensional spin chains and quasi-one-dimensional two-leg spin ladders. The calculated results show that with the appropriate partition of the studied systems the BCCC3 method can yield quite satisfactory ground-state energies for these spin systems.     

An exponential multireference wave-function Ansatz

An exponential multireference wave-function Ansatz is formulated. In accordance with the state universal coupled-cluster Ansatz of Jeziorski and Monkhorst [Phys. Rev. A 24, 1668 (1981)] the approach uses a reference specific cluster operator. In order to achieve state selectiveness the excitation- and reference-related amplitude indexing of the state universal Ansatz is replaced by an indexing which is based on excited determinants. There is no reference determinant playing a particular role. The approach is size consistent, coincides with traditional single-reference coupled cluster if applied to a single-reference, and converges to full configuration interaction with an increasing cluster operator excitation level. Initial applications on BeH2, CH2, Li2, and nH2 are reported.     

A CASSCF-CASPT2 study of the excited-state intramolecular proton transfer reaction in 1-amino-3-propenal using different active spaces

In this work we analyze how the choice of the active space in the CASSCF (the complete-active-space multiconfiguration self-consistent-field method) and CASPT2 (the second-order perturbation theory based on the CASSCF reference wave function) calculations affects the computed potential energy curves (PECs) for the intramolecular proton transfer reaction in the ground state and the two lowest lying singlet excited states of 1-amino-3-propenal. As anticipated, the results revealed that, qualitatively, the proton transfer in the different states can be correctly described even by minimal active spaces, which include the orbitals involved in the electronic excitation of the considered state and the antibonding sigma orbital corresponding to the bond formed by the molecule with the migrating hydrogen atom. However, quantitatively, the relative energies of the two tautomers and the energy barriers computed at the CASSCF level change when the active space is increased, indicating importance of the dynamic electron correlation. Introducing the dynamic correlation effects via CASPT2 makes the calculated energy parameters more uniform among the different active spaces. The analysis suggested certain optimal active spaces for studying proton transfer reactions in systems similar to 1-amino-3-propenal. The PEC calculations for excited states showed that the results are sensitive to the molecular geometries used in the calculations, particularly near the transition point. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1422–1431 (1999)     

Valence bond theory for chemical dynamics

This essay provides a perspective on several issues in valence bond theory: the physical significance of semilocal bonding orbitals, the capability of valence bond concepts to explain systems with multireferences character, the use of valence bond theory to provide analytical representations of potential energy surfaces for chemical dynamics by the method of semiempirical valence bond potential energy surfaces (an early example of specific reaction parameters), by multiconfiguration molecular mechanics, by the combined valence bond-molecular mechanics method, and by the use of valence bond states as coupled diabatic states for describing electronically nonadiabatic processes (photochemistry). The essay includes both ab initio and semiempirical approaches.     

Theoretical study of the H(2) reaction with a Pt(4) (111) cluster

The C(s) symmetry reaction of the H(2) molecule on a Pt(4) (111) clusters, has been studied using ab initio multiconfiguration self-consistent field plus extensive multireference configuration interaction variational and perturbative calculations. The H(2) interaction by the vertex and by the base of a tetrahedral Pt(4) cluster were studied in ground and excited triplet and singlet states (closed and open shells), where the reaction curves are obtained through many avoided crossings. The Pt(4) cluster captures and activates the hydrogen molecule; it shows a similar behavior compared with other Pt(n) (n=1,2,3) systems. The Pt(4) cluster in their lowest five open and closed shell electronic states: (3)B(2), (1)B(2), (1)A(1) (3)A(1), (1)A(1), respectively, may capture and dissociate the H(2) molecule without activation barriers for the hydrogen molecule vertex approach. For the threefolded site reaction, i.e., by the base, the situation is different, the hydrogen adsorption presents some barriers. The potential energy minima occur outside and inside the cluster, with strong activation of the H-H bond. In all cases studied, the Pt(4) cluster does not absorb the hydrogen molecule.     

A full-dimensional coupled-surface study of the photodissociation dynamics of ammonia using the multiconfiguration time-dependent Hartree method

Full-dimensional quantum mechanical computations are carried out to investigate the photodissociation dynamics of A? state NH(3) and ND(3) using the multiconfiguration time-dependent Hartree (MCTDH) method with recently developed coupled ab initio potential energy surfaces (PESs) [Z. H. Li, R. Valero, and D. G. Truhlar, Theor. Chim. Acc. 118, 9 (2007)]. To use the MCTDH method efficiently the PESs are represented as based on the high-dimensional model representation. The A? ← X? absorption spectra for both isotopomers were calculated for the zeroth vibrational state of the ground electronic state. With a view to treating larger systems, Jacobi coordinates are used. Computations on the coupled PES are carried out for two-, three-, five-, and six-dimensional model systems to understand the validity of reduced-dimensional calculations. In addition to the fully coupled calculations, the effect of nonadiabatic coupling on absorption spectra is shown by propagating the initial wavepacket only in the A? electronic state. The calculated absorption spectra are shown to be in good agreement with available theoretical and experimental observations. Comparisons with calculations using Radau and valence coordinates show the effect of including the symmetry of the system explicitly. Finally, branching ratios for loss of a hydrogen atom via the two available channels are calculated. These predict that the nonadiabatic product increases with the dimension of the calculations and confirm the importance of the full-dimensional calculations.     

On the computation of excited states with MCSCF methods

We discuss the theoretical and practical problems arising when trying to compute excited states of nonrelativistic electrons in a molecular system, by multiconfiguration (MCSCF) methods. These nonlinear models approximate the linear Schrödinger theory and are a generalization of the well-known Hartree–Fock approach. Due to the MCSCF nonlinearity, a theoretical definition of what should be a MCSCF excited state is not clear at all, contrarily to the ground state case. We compare various definitions used in Quantum Chemistry. We in particular stress that some defects may lead to important computational problems, already observed in Quantum Chemistry (root flipping). We then present a definition of MCSCF excited states based on a solid mathematical ground and compare it with the most used methods. This new definition leads to a completely new algorithm for computing the first excited state, which was proposed and tested in a collaboration with Cancès and Galicher. Numerical results are provided for the simple case of two-electron systems, as an illustration of the possible issues which can arise as consequences of the nonlinearity of the MCSCF method.