Multireference Electronic Structure Research Articles

Quantum wavepacket ab initio molecular dynamics: Generalizations using an extended Lagrangian treatment of diabatic states coupled through multireference electronic structure

We present a generalization to our previously developed quantum wavepacket ab initio molecular dynamics (QWAIMD) method by using multiple diabatic electronic reduced single particle density matrices, propagated within an extended Lagrangian paradigm. The Slater determinantal wavefunctions associated with the density matrices utilized may be orthogonal or nonorthogonal with respect to each other. This generalization directly results from an analysis of the variance in electronic structure with quantum nuclear degrees of freedom. The diabatic electronic states are treated here as classical parametric variables and propagated simultaneously along with the quantum wavepacket and classical nuclei. Each electronic density matrix is constrained to be N-representable. Consequently two sets of new methods are derived: extended Lagrangian-QWAIMD (xLag-QWAIMD) and diabatic extended Lagrangian-QWAIMD (DxLag-QWAIMD). In both cases, the instantaneous potential energy surface for the quantum nuclear degrees of freedom is constructed from the diabatic states using an on-the-fly nonorthogonal multireference formalism. By introducing generalized grid-based electronic basis functions, we eliminate the basis set dependence on the quantum nucleus. Subsequent reuse of the two-electron integrals during the on-the-fly potential energy surface computation stage yields a substantial reduction in computational costs. Specifically, both xLag-QWAIMD and DxLag-QWAIMD turn out to be about two orders of magnitude faster than our previously developed time-dependent deterministic sampling implementation of QWAIMD. Energy conservation properties, accuracy of the associated potential surfaces, and vibrational properties are analyzed for a family of hydrogen bonded systems.

Comparison of some multireference electronic structure methods in illustrative applications

The performances of several multireference electronic structure methods including complete active space self-consistent field (CASSCF)-based second-order perturbation theory (CASPT2), multireference configuration interaction with single and double excitations (MR-CISD), MR-CISD with the Davidson correction (MR-CISD+Q), and the CASSCF-based block-correlated coupled cluster method (CAS-BCCC4) we developed recently are compared by applying them to study several different chemical problems involving computation of ground state potential energy surfaces, the singlet-triplet gaps in diradicals, reaction barriers, and the excitation energies of low-lying excited states. Comparison with the results from other highly accurate theoretical methods or the available experimental data demonstrate that for all the problems studied, the overall performance of CAS-BCCC4 is competitive with that of MR-CISD+Q, and better than that of CASPT2 and MR-CISD methods. Thus the CAS-BCCC4 approach is expected to be a promising theoretical method for quantitative descriptions of the electronic structures of molecules with noticeable multireference character.

Spectroscopy, Structure, and Ionization Energy of BeOBe

Electronic transitions of BeOBe have been investigated using laser-induced fluorescence and resonance enhanced multiphoton ionization techniques in the 27000-33000 cm-1 range. Vibronic progressions observed in these spectra were assigned to the symmetric and antisymmetric stretching vibrations in the excited electronic state. The nuclear spin statistics of the ground state, observed in the intensity patterns of rotationally resolved spectra, confirmed that the molecule is symmetric (BeOBe) and has 1 Sigma(g)+ symmetry. Analysis of the rotational structure yielded a value of 1.396(3) A for the BeO bond length. Ground state vibrational frequencies were determined using stimulated emission pumping. Photoionization efficiency curves were recorded that yielded a value of 8.119(5) eV for the BeOBe ionization energy. Multireference electronic structure calculations have been used to predict molecular constants and explore the orbital compositions of the ground and excited states.

High-performance ab initio density matrix renormalization group method: Applicability to large-scale multireference problems for metal compounds

This article presents an efficient and parallelized implementation of the density matrix renormalization group (DMRG) algorithm for quantum chemistry calculations. The DMRG method as a large-scale multireference electronic structure model is by nature particularly efficient for one-dimensionally correlated systems, while the present development is oriented toward applications for polynuclear transition metal compounds, in which the macroscopic one-dimensional structure of electron correlation is absent. A straightforward extension of the DMRG algorithm is proposed with further improvements and aggressive optimizations to allow its application with large multireference active space, which is often demanded for metal compound calculations. Special efficiency is achieved by making better use of sparsity and symmetry in the operator and wave function representations. By accomplishing computationally intensive DMRG calculations, the authors have found that a large number of renormalized basis states are required to represent high entanglement of the electron correlation for metal compound applications, and it is crucial to adopt auxiliary perturbative correction to the projected density matrix during the DMRG sweep optimization in order to attain proper convergence to the solution. Potential energy curve calculations for the Cr(2) molecule near the known equilibrium precisely predicted the full configuration interaction energies with a correlation space of 24 electrons in 30 orbitals [denoted by (24e,30o)]. The energies are demonstrated to be accurate to 0.6mE(h) (the error from the extrapolated best value) when as many as 10,000 renormalized basis states are employed for the left and right DMRG block representations. The relative energy curves for [Cu(2)O(2)](2+) along the isomerization coordinate were obtained from DMRG and other correlated calculations, for which a fairly large orbital space (32e,62o) is modeled as a full correlation space. The DMRG prediction nearly overlaps with the energy curve from the coupled cluster with singles, doubles, and perturbative triple [CCSD(T)] calculations, while the multireference complete active space self-consistent field (CASSCF) calculations with the small reference configuration (8e,8o) are found to overestimate the biradical character of the electronic state of [Cu(2)O(2)](2+) according to the one-electron density matrix analysis.

Theoretical rate coefficients for the reaction of methyl radical with hydroperoxyl radical and for methylhydroperoxide decomposition

The kinetics of the CH3+HO2 bimolecular reaction and the thermal decomposition of CH3OOH are studied theoretically. Direct variable reaction coordinate transition state theory (VRC-TST), coupled with high level multireference electronic structure calculations, is used to compute capture rates for the CH3+HO2 reaction and to characterize the transition state of the barrierless CH3O+OH product channel. The CH2O+H2O product channel and the CH3+HO2→CH4+O2 reaction are treated using variational transition state theory and the harmonic oscillator and rigid rotor approximations. Pressure dependence and product branching in the bimolecular and decomposition reactions are modeled using master equation simulations. The predicted rate coefficients for the major products channels of the bimolecular reaction, CH3O+OH and CH4+O2, are found to be in excellent agreement with values obtained in two recent modeling studies. The present calculations are also used to obtain rate coefficients for the CH3O+OH association/decomposition reaction.

The accuracy of molecular bond lengths computed by multireference electronic structure methods

We compare experimental R e values with computed R e values for 20 molecules using three multireference electronic structure methods, MCSCF, MR-SDCI, and MR-AQCC. Three correlation-consistent orbital basis sets are used, along with complete basis set extrapolations, for all of the molecules. These data complement those computed previously with single-reference methods. Several trends are observed. The SCF R e values tend to be shorter than the experimental values, and the MCSCF values tend to be longer than the experimental values. We attribute these trends to the ionic contamination of the SCF wave function and to the corresponding systematic distortion of the potential energy curve. For the individual bonds, the MR-SDCI R e values tend to be shorter than the MR-AQCC values, which in turn tend to be shorter than the MCSCF values. Compared to the previous single-reference results, the MCSCF values are roughly comparable to the MP4 and CCSD methods, which are more accurate than might be expected due to the fact that these MCSCF wave functions include no extra-valence electron correlation effects. This suggests that static valence correlation effects, such as near-degeneracies and the ability to dissociate correctly to neutral fragments, play an important role in determining the shape of the potential energy surface, even near equilibrium structures. The MR-SDCI and MR-AQCC methods predict R e values with an accuracy comparable to, or better than, the best single-reference methods (MP4, CCSD, and CCSD(T)), despite the fact that triple and higher excitations into the extra-valence orbital space are included in the single-reference methods but are absent in the multireference wave functions. The computed R e values using the multireference methods tend to be smooth and monotonic with basis set improvement. The molecular structures are optimized using analytic energy gradients, and the timings for these calculations show the practical advantage of using variational wave functions for which the Hellmann–Feynman theorem can be exploited.

Electronic Structure of the Acetonitrile and Acetonitrile Dimer Anions: A Topological Investigation

Acetonitrile molecules are known for their intriguing ability to accommodate an excess electron in either a diffuse dipole-bound orbital, away from the valence electrons, or in its valence orbitals, depending on the environment. In this work, we report a computational investigation of the monomer and dimer acetonitrile anions, with the main goal of gaining further insight into the unusual electronic structure of these species. To this end, the topology of the electron density distribution has been examined in detail with the quantum theory of atoms in molecules (AIM). The excess electron is found to affect the topology of the electron density very differently for two dipole-bound-electron isomers of the acetonitrile dimer anion: for the head-to-tail isomer, the electron density simply decays away from the atomic nuclei, and the presence of the excess electron only manifests itself in the Laplacian of the electron density as a very diffuse region of "dipole-bound" charge concentration; in contrast, for the "solvated-electron" head-to-head isomer, a maximum of electron density without a corresponding atomic nucleus is observed, which topologically corresponds to a pseudo-atom of electron density. The acetonitrile dimer appears to be the smallest solvent cluster anion to exhibit such a non-nuclear attractor due to the presence of a solvated electron. Although the "solvated-electron" isomer is thermodynamically less stable than the head-to-tail isomer at 0 K, its floppy nature leads to a higher vibrational entropy that makes it the most stable acetonitrile dimer, anionic or neutral, above 150 K. As for the acetonitrile dimer anion with a valence-bound electron, its structure is characterized by acetonitrile molecules connected to each other at the cyanide carbon atoms; the AIM analysis reveals that, although this C-C bond is relatively weak, with an estimated bond order of 0.6, it possesses genuine covalent character and is not a "pseudo-bond" as previously speculated. We also report the first multireference electronic structure calculations of the valence-bound-electron acetonitrile monomer and dimer anions, the highest-level calculations of these species to date. The acetonitrile radical anion is unstable in the gas phase and is topologically characterized by a radical-like nonbonded charge concentration located at the cyanide carbon atom. Based on the results of the AIM analysis, the previously proposed resonance description of the valence-bound-electron acetonitrile anion is refined, and a new resonance description of the dimer anion is proposed. Overall, this work demonstrates the rich topological variety of the excess electron interacting with acetonitrile molecules, which manifests itself as charge concentrations, pseudo-atoms, and covalent bonds.

Analysis and prediction of absorption band shapes, fluorescence band shapes, resonance Raman intensities, and excitation profiles using the time-dependent theory of electronic spectroscopy

A general method for the simulation of absorption (ABS) and fluorescence band shapes, resonance-Raman (rR) spectra, and excitation profiles based on the time-dependent theory of Heller is discussed. The following improvements to Heller's theory have been made: (a) derivation of new recurrence relations for the time-dependent wave packet overlap in the case of frequency changes between the ground and electronically excited states, (b) a new series expansion that gives insight into the nature of Savin's preresonance approximation, (c) incorporation of inhomogeneous broadening effects into the formalism at no additional computational cost, and (d) derivation of a new and simple short-time dynamics based equation for the Stokes shift that remains valid in the case of partially resolved vibrational structure. Our implementation of the time-dependent theory for the fitting of experimental spectra and the simulation of model spectra as well as the quantum mechanical calculation of the model parameters is discussed. The implementation covers all electronic structure approaches which are able to deliver ground- and excited-state energies and transition dipole moments. The technique becomes highly efficient if analytic gradients for the excited-state surface are available. In this case, the computational cost for the simultaneous prediction of ABS, fluorescence, and rR spectra is equal to that of a single excited-state geometry optimization step while the limitations of the short-time dynamics approximation are completely avoided. As a test case we discuss the well-known case of the strongly allowed 1 (1)A(g) --> 1 (1)B(u) transition in 1,3,5 trans-hexatriene in detail using method ranging from simple single-reference treatments to elaborate multireference electronic structure approaches. At the highest computational level, the computed spectra show the best agreement that has so far been obtained with quantum chemical methods for this problem.

Kinetics of the Reaction of Methyl Radical with Hydroxyl Radical and Methanol Decomposition

The CH3 + OH bimolecular reaction and the dissociation of methanol are studied theoretically at conditions relevant to combustion chemistry. Kinetics for the CH3 + OH barrierless association reaction and for the H + CH2OH and H + CH3O product channels are determined in the high-pressure limit using variable reaction coordinate transition state theory and multireference electronic structure calculations to evaluate the fragment interaction energies. The CH3 + OH --> 3CH2 + H2O abstraction reaction and the H2 + HCOH and H2 + H2CO product channels feature localized dynamical bottlenecks and are treated using variational transition state theory and QCISD(T) energies extrapolated to the complete basis set limit. The 1CH2 + H2O product channel has two dynamical regimes, featuring both an inner saddle point and an outer barrierless region, and it is shown that a microcanonical two-state model is necessary to properly describe the association rate for this reaction over a broad temperature range. Experimental channel energies for the methanol system are reevaluated using the Active Thermochemical Tables (ATcT) approach. Pressure dependent, phenomenological rate coefficients for the CH3 + OH bimolecular reaction and for methanol decomposition are determined via master equation simulations. The predicted results agree well with experimental results, including those from a companion high-temperature shock tube determination for the decomposition of methanol.

Conical intersections involving the dissociative1πσ* state in 9H-adenine: a quantum chemical ab initio study

The conical intersections of the dissociative 1pisigma* excited state with the lowest 1pipi* excited state and the electronic ground state of 9H-adenine have been investigated with multireference electronic structure calculations. Adiabatic and quasidiabatic potential energy surfaces and coupling elements were calculated as a function of the NH stretch coordinate of the azine group and the out-of-plane angle of the hydrogen atom, employing MultiReference Configuration-Interaction (MRCI) as well as Complete-Active-Space Self-Consistent-Field (CASSCF) methods. Characteristic properties of the 1pipi*-1pisigma* and 1pisigma*-S0 conical intersections, such as the diabatic-to-adiabatic mixing angle, the geometric phase of the adiabatic electronic wavefunctions, the derivative coupling, as well as adiabatic and diabatic transition dipole moment surfaces were investigated in detail. These data are a prerequisite for future quantum wavepacket simulations of the photodissociation and internal-conversion dynamics of adenine.

THE EXOTHERMIC PNC → PCN REACTION

PCN and PNC are possible interstellar species that have not been experimentally characterized. With various ab initio methods, including multireference and restricted open-shell single-reference electronic structure theory, the PCN/PNC species and the transition state for the isomerization reaction PCN ↔ PNC have been studied. The Dunning series of correlation-consistent basis sets, cc-pVXZ and aug-cc-pVXZ (X = T and Q), have been used. Geometries, total energies, dipole moments, harmonic vibrational frequencies, infrared intensities, and zero-point vibrational energies are reported for the PCN/PNC isomers and the transition state. Both PCN and PNC are linear with 3Σ- ground states, and linear [Formula: see text] is predicted to lie 13.7 kcal mol-1 (13.5 kcal mol-1 with ZPVE correction) above linear [Formula: see text] at the aug-cc-pVQZ CCSD(T) level of theory. The CN bond distance in [Formula: see text] is predicted to be 1.174 Å, only 0.002 Å longer than the experimental value of 1.172 Å for diatomic CN (X2Σ+, suggesting that CN has triple bond character in [Formula: see text]. The isomerization transition state is found to be cyclic [Formula: see text], with angles θ e ( PCN ) = 82.2°, θ e ( CNP ) = 63.1°, and θ e ( NPC ) = 34.7°. The isomerization barrier is predicted to be 35.7 kcal mol-1 (34.5 kcal mol-1 with ZPVE correction) relative to linear [Formula: see text]. The predicted dipole moments are substantial, 2.79 debye (polarity + PCN -) and 2.51 debye (polarity + PNC -).

On the choice of reference in multi-reference electronic structure theory: minimal references for bond breaking

Minimal reference space definitions are presented for complete active space self-consistent field (CASSCF) and restricted active space self-consistent field (RASSCF) descriptions of bond-breaking reactions and compared to CASSCF wavefunctions using full-valence and one-to-one active spaces. Potential energy curves for reactions breaking both single and multiple bonds are computed using multi-reference perturbation theory and multi-reference configuration interaction based upon these reference wavefunctions, and results are compared to full configuration interaction benchmark curves. This allows one to ascertain the ability of minimal reference spaces to recover the strong non-dynamical correlation effects in these systems by comparison to results with larger reference spaces and to the exact results for a given basis set. Minimal reference spaces, at a fraction of the cost, typically perform on par with much larger reference spaces in computations which also include dynamical electron correlation.

Low-lying electronic states of FeNC and FeCN: a theoretical journey into isomerization and quartet/sextet competition.

With several levels of multireference and restricted open-shell single-reference electronic structure theory, optimum structures, relative energetics, and spectroscopic properties of the low-lying (6)Delta, (6)Pi, (4)Delta, (4)Pi, and (4)Sigma(-) states of linear FeNC and FeCN have been investigated using five contracted Gaussian basis sets ranging from Fe[10s8p3d], C/N[4s2p1d] to Fe[6s8p6d3f2g1h], C/N[6s5p4d3f2g]. Based on multireference configuration interaction (MRCISD+Q) results with a correlation-consistent polarized valence quadruple-zeta (cc-pVQZ) basis set, appended with core correlation and relativistic corrections, we propose the relative energies: T(e)(FeNC), (6)Delta(0)<(6)Pi (2300 cm(-1))<(4)Delta (2700 cm(-1))<(4)Pi (4200 cm(-1))<(4)Sigma(-); and T(e)(FeCN), (6)Delta(0)<(6)Pi (1800 cm(-1))<(4)Delta (2500 cm(-1))<(4)Pi (2900 cm(-1))<(4)Sigma(-). The (4)Delta and (4)Pi states have massive multireference character, arising mostly from 11sigma-->12sigma promotions, whereas the sextet states are dominated by single electronic configurations. The single-reference CCSDT-3 (coupled cluster singles and doubles with iterative partial triples) method appears to significantly overshoot the stabilization of the quartet states provided by both static and dynamical correlation. The (4,6)Delta and (4,6)Pi states of both isomers are rather ionic, and all have dipole moments near 5 D. On the ground (6)Delta surface, FeNC is predicted to lie 0.6 kcal mol(-1) below FeCN, and the classical barrier for isocyanide/cyanide isomerization is about 6.5 kcal mol(-1). Our data support the recent spectroscopic characterization by Lei and Dagdigian [J. Chem. Phys. 114, 2137 (2000)] of linear (6)Delta FeNC as the first experimentally observed transition-metal monoisocyanide. Their assignments for the ground term symbol, isotopomeric rotational constants, and the Fe-N omega(3) stretching frequency are confirmed; however, we find rather different structural parameters for (6)Delta FeNC:r(e)(Fe-N)=1.940 A and r(N-C)=1.182 A at the cc-pVQZ MRCISD+Q level. Our results also reveal that the observed band of FeNC originating at 27 236 cm(-1) should have an analog in FeCN near 23 800 cm(-1) of almost equal intensity. Therefore, both thermodynamic stability and absorption intensity factors favor the eventual observation of FeCN via a (6)Pi<--(6)Delta transition in the near-UV.

High-level multireference methods in the quantum-chemistry program system COLUMBUS: Analytic MR-CISD and MR-AQCC gradients and MR-AQCC-LRT for excited states, GUGA spin–orbit CI and parallel CI density

Development of several new computational approaches within the framework of multi-reference ab initio molecular electronic structure methodology and their implementation in the COLUMBUS program system are reported. These new features are: calculation of the analytical MR-CI gradient for excited states based on state-averaged MCSCF orbitals, the extension of the MR-ACPF/AQCC methods to excited states in the framework of linear-response theory, spin–orbit CI for molecules containing heavy atoms and the development of a massively-parallel code for the computation of the one- and two-particle density matrix elements. Illustrative examples are given for each of these cases.