Improved Virtual Orbital-complete Active Space Configuration Interaction Research Articles

Description of quasidegenerate electronic states exhibiting avoided crossing

ABSTRACTThe feasibility of the multiconfiguration quasidegenerate perturbation theory (MCQDPT) with improved virtual orbital-complete active space configuration interaction (IVO-CASCI) reference function is demonstrated by scrutinising the interaction potential of LiCl and AlX (X=He and Ne) and analysing the avoided crossing along the bond dissociation, representing a hard challenge for any given electronic structure approach. IVO-MCQDPT procedure is capable of providing very close agreement of the computed energy surfaces and spectroscopic parameters with the reference values at the expense of low computational labour showing that the present method is valuable for dealing with the avoided curve crossing problem.

Improved virtual orbitals in state specific multireference perturbation theory for prototypes of quasidegenerate electronic structure.

The state-specific multireference perturbation theory (SSMRPT) with an improved virtual orbital complete active space configuration interaction (IVO-CASCI) reference function [called as IVO-SSMRPT] is used to investigate the energy surface, geometrical parameters, molecular properties of spectroscopic interest for the systems/situations [such as BeH2, BeCH2, MgCH2, Si2H4, unimolecular dissociation of H2CO, and intramolecular reaction pathways of 1,3-butadiene] where the effect of quasidegeneracy cannot be neglected. The merit of using the IVO-CASCI rather than complete active space self-consistent field (CASSCF) is that it is free from iterations beyond those in the initial SCF calculation and the convergence difficulties that plague CASSCF calculations with increasing size of the CAS. While IVO-CASCI describes the non-dynamical correlation, the SSMRPT scheme is a good second-order perturbative approximation to account for the rest of the correlation energy. Our IVO-SSMRPT method is instrumental in avoiding intruder states in an size-extensive manner and allows the revision of the content of wave function in the model space. It can treat model as well as real systems with predictive accuracy, as is evident from the fairly nice accordance between our estimates, and high-level theoretical results. Our estimates also corroborate well with some experimental findings.

Four-Component Relativistic State-Specific Multireference Perturbation Theory with a Simplified Treatment of Static Correlation.

The relativistic multireference (MR) perturbative approach is one of the most successful tools for the description of computationally demanding molecular systems of heavy elements. We present here the ground state dissociation energy surfaces, equilibrium bond lengths, harmonic frequencies, and dissociation energies of Ag2, Cu2, Au2, and I2 computed using the four-component (4c) relativistic spinors based state-specific MR perturbation theory (SSMRPT) with improved virtual orbital complete active space configuration interaction (IVO-CASCI) functions. The IVO-CASCI method is a simple, robust, useful and lower cost alternative to the complete active space self-consistent field approach for treating quasidegenerate situations. The redeeming features of the resulting method, termed as 4c-IVO-SSMRPT, lies in (i) manifestly size-extensivity, (ii) exemption from intruder problems, (iii) the freedom of convenient multipartitionings of the Hamiltonian, (iv) flexibility of the relaxed and unrelaxed descriptions of the reference coefficients, and (v) manageable cost/accuracy ratio. The present method delivers accurate descriptions of dissociation processes of heavy element systems. Close agreement with reference values has been found for the calculated molecular constants indicating that our 4c-IVOSSMRPT provides a robust and economic protocol for determining the structural properties for the ground state of heavy element molecules with eloquent MR character as it treats correlation and relativity on equal footing.

A simplified ab initio treatment of diradicaloid structures produced from stretching and breaking chemical bonds.

The present investigation reports on the prospect of using state specific multireference perturbation theory (SSMRPT) with an improved virtual orbital complete active space configuration interaction (IVO-CASCI) reference function (IVO-SSMRPT) to generate potential energy surfaces (PESs) for molecular systems [such as CH4, C2H6, C2H4, H2O2, LiH, and KN] by stretching and breaking of suitable bonds with modest basis sets. We have also revisited the dissociation energy profile of triplet ketene which exhibits a step-like structure in the observed rate. The application of the method has also been made to the ionization energies of H2O. Although the perturbative corrections are obtained by the diagonalization of the effective Hamiltonian, in IVO-SSMRPT, only one physically relevant solution is achievable. It is parameter free and does not require any threshold to avoid the intruder problem. It is strictly size-extensive and size-consistent provided that local orbitals are used. The PESs obtained with our approach are smooth all along the reaction path. Our estimates are in close agreement with the available reference data indicating that IVO-SSMRPT is a robust paradigm for the accurate computation of ground, excited and ionized states as it captures the mutual inter-play of different flavors of correlation effects in a balanced and accurate way.

Relativistic state-specific multireference perturbation theory incorporating improved virtual orbitals: Application to the ground state single-bond dissociation.

Using four-component (4c) relativistic spinors, we present a computationally economical relativistic ab initio method for molecular systems employing our recently proposed second-order state-specific multireference perturbation theory (SSMRPT) incorporating the improved virtual orbital-complete active space configuration interaction (IVO-CASCI) reference wavefunction. The resulting method, 4c-IVO-SSMRPT [calculate one state at a time] is tested in pilot calculations on the homonuclear dimers including Li(2), Na(2), K(2), Rb(2), F(2), Cl(2), and Br(2) through the computations of the ground state potential energy curves (PECs). As SSMRPT curbs intruder effects, 4c-IVO-SSMRPT is numerically stable. To our knowledge, the SSMRPT in the 4c relativistic framework has not been explored in the past. Selective spectroscopic constants that are closely related to the correct shape and accuracy of the energy surfaces have been extracted from the computed PECs. For the halogen molecules, a relativistic destabilization of the bond has been found. Relativistic and electron correlation effects need to be incorporated to get reliable estimates. Our results are in good accordance with reference theoretical and experimental data which manifests the computational accuracy and efficiency of the new 4c-IVO-SSMRPT method. The method opens for an improved description of MR systems containing heavy elements. The inexpensiveness of IVO-CASCI makes 4c-IVO-SSMRPT method promising for studies on large systems of heavy elements.

Theoretical Studies of the Ground and Excited State Structures of Stilbene

Optimized geometries are evaluated for the ground and low lying excited states of cis-stilbene, trans-stilbene, and 4a,4b-dihydrophenanthrene (DHP) from calculations performed with the improved virtual orbital, complete active space configuration interaction (IVO-CASCI) method. The calculations indicate that a nonplanar conformer of trans-stilbene is the most stable among the isomers. The calculated ground and low lying excited state geometries agree well with experiment and with prior theoretical estimates where available. Our IVO-CASCI based multireference Möller-Plesset (MRMP) computations place the (1)B(u) state of trans stilbene to be ∼4.0 eV above the ground X(1)A(g) state, which is in accord with experiment and with earlier theoretical estimates. The 1(1)B(u) state of trans-stilbene can be represented by the highest occupied molecular orbital (HOMO) → lowest unoccupied molecular orbital (LUMO) transition (ionic type) from the ground state, whereas its 2(1)B(u) state is dominated by the HOMO → LUMO+1 and HOMO-1 → LUMO transitions (covalent type). Likewise, the 1(1)B and 2(1)B states of cis-stilbene and DHP are also found to be of ionic and covalent types, respectively.

Application of an efficient multireference approach to free-base porphin and metalloporphyrins: Ground, excited, and positive ion states

The improved virtual orbital-complete active space configuration interaction (IVO-CASCI) method is applied to determine the geometries of the ground state of free-base porphin and its metal derivatives, magnesium and zinc porphyrins. The vertical excitation energies and ionization potentials are computed at these optimized geometries using an IVO-based version of multireference Möller-Plesset (IVO-MRMP) perturbation theory. The geometries and excitation energies obtained from the IVO-CASCI and IVO-MRMP methods agree well with experiment and with other correlated many-body methods. We also provide the ground state vibrational frequencies for free-base porphin and Mg-porphyrin. All frequencies are real in contrast to self-consistent field treatments which yield an imaginary frequency. Ground state normal mode frequencies (scaled) of free-base porphin and magnesium porphyrin from IVO-CASCI and complete active space self-consistent field methods are quite similar and are consistent with Becke-Slater-Hartree-Fock exchange and Lee-Yang-Parr correlation density functional theory calculations and with experiment. In addition, geometries are determined for low-lying excited state triplets and for positive ion states of the molecules. To our knowledge, no prior experimental and theoretical data are available for these excited state geometries of magnesium and zinc porphyrins. Given that the IVO-CASCI and IVO-MRMP computed geometries and excitation energies agree favorably with experiment and with available theoretical data, our predicted excited state geometries should be equally accurate.

Prediction of electronic structure of organic radicaloid anions using efficient, economical multireference gradient approach

The improved virtual orbital-complete active space configuration interaction (IVO-CASCI) method enables an economical and reasonably accurate treatment of static correlation in systems with significant multireference character, even when using a moderate basis set. This IVO-CASCI method supplants the computationally more demanding complete active space self-consistent field (CASSCF) method by producing comparable accuracy with diminished computational effort because the IVO-CASCI approach does not require additional iterations beyond an initial SCF calculation, nor does it encounter convergence difficulties or multiple solutions that may be found in CASSCF calculations. Our IVO-CASCI analytical gradient approach is applied to compute the equilibrium geometry for the ground and lowest excited state(s) of the theoretically very challenging 2,6-pyridyne, 1,2,3-tridehydrobenzene and 1,3,5-tridehydrobenzene anionic systems for which experiments are lacking, accurate quantum calculations are almost completely absent, and commonly used calculations based on single reference configurations fail to provide reasonable results. Hence, the computational complexity provides an excellent test for the efficacy of multireference methods. The present work clearly illustrates that the IVO-CASCI analytical gradient method provides a good description of the complicated electronic quasi-degeneracies during the geometry optimization process for the radicaloid anions. The IVO-CASCI treatment produces almost identical geometries as the CASSCF calculations (performed for this study) at a fraction of the computational labor. Adiabatic energy gaps to low lying excited states likewise emerge from the IVO-CASCI and CASSCF methods as very similar. We also provide harmonic vibrational frequencies to demonstrate the stability of the computed geometries.

Studies on m-benzyne and phenol via improved virtual orbital-complete active space configuration interaction (IVO-CASCI) analytical gradient method

Improved virtual orbital-complete active space configuration interaction (IVO-CASCI) analytical gradient theory has been used to investigate geometrical parameters, vibrational frequencies and excitation energies of m-benzyne and phenol using different reference spaces and basis sets. Compared to the results obtained via CASSCF treatments, it has been found that the IVO-CASCI gradient method provides very satisfactory results with low computational cost. IVO-CASCI values compare reasonably well with the earlier established theoretical results and experimental values whenever available.

Molecular applications of analytical gradient approach for the improved virtual orbital-complete active space configuration interaction method

The improved virtual orbital-complete active space configuration interaction (IVO-CASCI) method is extended to determine the geometry and vibrational frequencies for ground and excited electronic states using an analytical total energy gradient scheme involving both first and second order analytical derivatives. Illustrative applications consider the ground state geometries of the benzene (C(6)H(6)), biphenyl (C(12)H(10)), and alanine dipeptide (CH(3)CONHCHCH(3)CONHCH(3)) molecules. In addition, the IVO-CASCI geometry optimization has been performed for the first excited singlet ((1)B(2u)) and triplet states ((3)B(1u)) of benzene to assess its applicability for excited and open-shell systems. The D(6h) symmetry benzene triplet optimization produces a saddle point, and a descent along the unstable mode produces the stable minimum. Comparisons with Hartree-Fock, second order Moller-Plesset perturbation theory, complete active space self-consistent field (CASSCF), and density functional theory demonstrate that the IVO-CASCI approach generally fares comparable to or better for all systems studied. The vibrational frequencies of the benzene and biphenyl molecules computed with the analytical gradient based IVO-CASCI method agree with the experiment and with other accurate theoretical estimates. Satisfactory agreement between our results, other benchmark calculations, and available experiment demonstrates the efficacy and potential of the method. The close similarity between CASSCF and IVO-CASCI optimized geometries and the greater computational efficiency of the IVO-CASCI method suggests the replacement of CASSCF treatments by the IVO-CASCI approach, which is free from the convergence problems that often plague CASSCF treatments.

Geometry optimization using improved virtual orbitals: A complete active space numerical gradient approach

The improved virtual orbital-complete active space configuration interaction (IVO-CASCI) method is extended to enable geometry optimization and the calculation of vibrational frequencies for ground and excited states using numerical energy gradients. Applications consider the ground state geometries and vibrational frequencies of the Be2, LiF, H2S, and HCN molecules, as well as excited state properties for HCN, systems that are sufficiently complex to access the efficacy of the method. Comparisons with other standard approaches (self-consistent field, second order Moller-Plesset perturbation theory, complete active space self-consistent field, and coupled cluster singles and doubles methods) demonstrate that the numerical gradient version of the IVO-CASCI approach generally fares comparable to or better for all systems studied. The accurate estimates for the Be2 bond length and vibrational frequency are notable since many other computationally facile methods produce poor results.

A critical comparison of theoretical and experimental electronic spectrum and potential energy curves of HF molecule and its positive and negative ions

Although ab initio many-body methods can provide accurate predictions for most small systems, substantial effort is devoted to design and develop fairly accurate and computationally efficient ‘packageable’ methods for treating large molecular systems, where packageable implies a method that can be incorporated into widely distributed suites of electronic structure programs. Here, we provide further tests and illustrations of our recently developed improved virtual orbital-complete active space configuration interaction (IVO-CASCI) method, which is designed to supplant CIS and CASSCF approaches in electronic structure ‘packages’ because of greater computational efficiency without sacrificing accuracy. The IVO-CASCI method is used here to compute the ground, excited, positive, and negative ion potential energy curve of hydrogen fluoride. Additional dynamical correlation is incorporated by using IVO-CASCI wavefunctions as the initial approximation in selected further effective valence shell Hamiltonian computations for HF and its ions. The excellent agreement between the theory, experiment, and some benchmark calculations for several ground, excited, and ion states of HF reinforces the claim that the IVO-CASCI method is a viable alternate packageable many-body method for ground, excited, and other open-shell states of small to large molecular systems.