A multireference perturbation theory study on the vertical electronic spectrum of thiophene

The vertical electronic spectrum of the thiophene molecule is investigated by means of second and third order multireference perturbation theory (NEVPT). Single-state and quasi-degenerate NEVPT calculations of more than 25 singlet excited states have been performed. The study is addressed to the theoretical characterization of the four lowest-energy valence states, as well as the 3s, 3p and 3d Rydberg states. In addition, the excitation energies of two and valence states are also reported. For almost all the excited states, coupled cluster calculations (CCSD and CCSDR(3)) have been also carried out, using the same geometry and basis set used for the NEVPT ones, in order to make the comparison between the results of the two methods meaningful. A remarkable accordance between the NEVPT and CC excitation energies is found. The present results, over all, confirm the experimental assignments but, above all, represent an important contribution to the assignments of some low-energy states, valence and Rydberg, for which a firm interpretation is not available in the literature.     

Excitation Energies of Canonical Nucleobases Computed by Multiconfigurational Perturbation Theories

In this computational work, we assessed the performance of ab initio multireference (MR) methods for the calculation of vertical excitation energies of five nucleobases: adenine, guanine, cytosine, thymine and uracil. In total, we have studied 38 singlet and 30 triplet excited states. Where possible we used the multireference configuration interaction (MRCI) method as a reference for various flavors of multireference perturbation theory to second order. In particular, we have benchmarked CASPT2, NEVPT2 and XMCQDPT2. For CASPT2, we have analyzed the single‐state, multistate (MS) and extended MS variants. In addition, we have assessed the effect of the ionization potential electron affinity (IPEA) shift. For NEVPT2, we have used the partially and the strongly contracted variants. Further, we have tested the commonly used RI‐CC2, RI‐ADC2 and EOM‐CCSD methods. Generally, we observe the following trends for singlet excited states: NEVPT2 is the closest MR method to MRCISD+Q, closely followed by CASPT2 with the default IPEA shift. The same trend is observed for triplet states, although NEVPT2 and CASPT2‐IPEA are getting closer. Interestingly, the n, π* singlet excited states were described more accurately than π, π* excited states, while for triplet states the trend is inverted except for NEVPT2. This work is an important benchmark for future photochemical investigations.     

DFT,DLPNO-CCSD(T), and NEVPT2 benchmark study of the reaction between ferrocenium and trimethylphosphine

The reaction between ferrocenium and trimethylphosphine was studied using density functional theory (DFT), domain-based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)), and N-electron valence state perturbation theory (NEVPT2). The accuracy of the DFT functionals decreases compared to the DLPNO-CCSD(T) level in the following order: M06-L > TPSS > M06, BLYP > PBE, PBE0, B3LYP > > PWPB95 > > DSD-BLYP. The roles of thermochemical, continuum solvation (SMD), and counterpoise corrections were evaluated. Grimme's D3 empirical dispersion correction is essential for all functionals studied except M06 and M06-L. The reliability of the frequency calculations performed directly within the SMD was confirmed. The systems showed no significant multireference character according to T₁ and T₂ diagnostics and the fractional occupation number (FOD) weighted electron density analysis. The multireference NEVPT2 calculations gave qualitatively valid conclusions about the reaction mechanism. However, a multireference approach is generally not recommended because it requires arbitrary chosen active spaces.     

New perspectives in multireference perturbation theory: the n-electron valence state approach

The n-electron valence state perturbation theory (NEVPT) is a form of multireference perturbation theory which is based on a zero order reference wavefunction of CAS-CI type (complete active space configuration interaction) and which is characterized by the utilization of correction functions (zero order wavefunctions external to the CAS) of multireference nature, obtained through the diagonalization of a suitable two-electron model Hamiltonian (Dyall’s Hamiltonian) in some well defined determinant spaces. A review of the NEVPT approach is presented, starting from the original second order state-specific formulation, going through the quasidegenerate multi-state extension and arriving at the recent implementations of the third order in the energy and of the internally contracted configuration interaction. The chief properties of NEVPT—size consistence and absence of intruder states—are analyzed. Finally, an application concerning the calculation of the vertical spectrum of the biologically important free base porphin molecule, is presented.     

All‐electron relativistic computations on the low‐lying electronic states,bond length,and vibrational frequency of CeF diatomic molecule with spin–orbit coupling effects

Ab initio all‐electron computations have been carried out for Ce⁺ and CeF, including the electron correlation, scalar relativistic, and spin–orbit coupling effects in a quantitative manner. First, the n‐electron valence state second‐order multireference perturbation theory (NEVPT2) and spin–orbit configuration interaction (SOCI) based on the state‐averaged restricted active space multiconfigurational self‐consistent field (SA‐RASSCF) and state‐averaged complete active space multiconfigurational self‐consistent field (SA‐CASSCF) wavefunctions have been applied to evaluations of the low‐lying energy levels of Ce⁺ with [Xe]4f¹5d¹6s¹ and [Xe]4f¹5d² configurations, to test the accuracy of several all‐electron relativistic basis sets. It is shown that the mixing of quartet and doublet states is essential to reproduce the excitation energies. Then, SA‐RASSCF(CASSCF)/NEVPT2 + SOCI computations with the Sapporo(‐DKH3)‐2012‐QZP basis set were carried out to determine the energy levels of the low‐lying electronic states of CeF. The calculated excitation energies, bond length, and vibrational frequency are shown to be in good agreement with the available experimental data. © 2018 Wiley Periodicals, Inc.     

Ab initio computation of the interaction energy curves for some low-lying states of CO which dissociate to ground-state3 P O and3 P C atoms

Summary We investigate the molecular electronic structure of the quintet states of CO which correspond to the C(³ P)+O(³ P) interaction at several levels of theory. We find the 1⁵⁺ state to be relatively deeply bound (D _e ca. 587 cm^–1) while the other quintets have relatively shallow potential wells (D _e<40 cm^–1) according to our multireference configuration interaction calculations which are counterpoise corrected for basis set superposition effects. Our results are in qualitative accord with the recent semiempirical estimates of Bussery and co-workers [(1989) Chem. Phys. 134:7].National Academy of Sciences, National Research Council, Air Force Astronautics Laboratory, Resident Research Associate 1987–89     

Iterative Multireference Configuration Interaction

Iterative multireference configuration interaction (IMRCI) is proposed. It is exploited to compute the electronic energies of H\begin{document}$_2$\end{document}O and CH\begin{document}$_2$\end{document} (singlet and triplet states) at equilibrium and non-equilibrium geometries. The potential energy curves of H\begin{document}$_2$\end{document}O, CH\begin{document}$_2$\end{document} (singlet and triplet states) and N\begin{document}$_2$\end{document} have also been calculated with IMRCI as well as the M?ller Plesset perturbation theory (MP2, MP3, and MP4), the coupled cluster method with single and double substitutions (CCSD), and CCSD with perturbative triples correction (CCSD(T)). These calculations demonstrate that IMRCI results are independent of the initial guess of configuration functions in the reference space and converge quickly to the results of the full configuration interaction. The IMRCI errors relative to the full configuration interaction results are at the order of magnitude of 10\begin{document}$^{-5}$\end{document} hartree within just 2-4 iterations. Further, IMRCI provides an efficient way to find on the potential energy surface the leading electron configurations which, as correct reference states, will be very helpful for the single-reference and multireference theoretical models to obtain accurate results.     

Calibration of the n-electron valence state perturbation theory approach

Extensive tests have been performed to benchmark and to compare with second-order perturbation theory based on a complete active space self-consistent field reference function (CASPT2), the recently developed n-electron valence state perturbation theory at second order (NEVPT2). Test calculations included the group fifteen diatomic molecules X(2) (X=N, P, As, and Sb) and the (4)S/(2)D and (4)S/(2)P splittings for the corresponding atoms, the (1)A(1)-(3)B(1) splittings for CH(2) and SiH(2), and the absorption spectra of pyrrole and of Cu(Imidazole)(2)(SH)(SH(2))(+), which is a model for plastocyanin. Comparisons with full configuration-interaction calculations and experimental data show that the accuracy of NEVPT2 is in most cases even better than CASPT2. Where intruder states hamper the CASPT2 calculations, NEVPT2 performs significantly better. Care is needed in the choice of active orbitals, for example in the calculation of the (4)S/(2)D and (4)S/(2)P splittings for the group fifteen atoms. This is due to the different treatment of orbitals belonging to the inactive or active spaces, making the NEVPT2 not invariant for the choice of active space, even in cases where the multiconfiguration self-consistent field energy is invariant.     

Multireference composite approaches for the accurate study of ground and excited electronic states: C2, N2, and O2

A multireference analog of the correlation consistent composite approach (MR-ccCA) based on complete active space with second-order perturbation theory (CASPT2) has been utilized in an investigation of the ground and valence excited states of C(2), N(2), and O(2). The performance of different second-order multireference perturbation theory methods including second-order n-electron valence state perturbation theory, second-order multireference M?ller-Plesset, and second-order generalized van Vleck perturbation theory has been analyzed as potential alternatives to CASPT2 within MR-ccCA. The MR-ccCA-P predicts spectroscopic constants with overall mean absolute deviations from experimental values of 0.0006 A?, 7.0 cm(-1), and 143 cm(-1) for equilibrium bond length (r(e)), harmonic frequency (ω(e)), and term values (T(e)), respectively, which are comparable to the predictions by more computationally costly multireference configuration interaction-based methods.     

Ab initio n-electron valence state perturbation theory study of the adiabatic transitions in carbonyl molecules: formaldehyde, acetaldehyde, and acetone

The application of the recently developed second-order n-electron valence state perturbation theory (NEVPT2) to small carbonyl molecules (formaldehyde, acetaldehyde, and acetone) is presented. The adiabatic transition energies are computed for the singlet and triplet n-->pi(*), pi-->pi(*), and sigma-->pi(*) states performing a full geometry optimization of the relevant states at the single state CASSCF level and taking into account the zero point energy correction in the harmonic approximation. The agreement with the known experimental values and with previously published high level calculations confirms that NEVPT2 is an efficient tool to be used for the interpretation of molecular electronic spectra. Moreover, different insight into the nature of the excited states has been obtained. Some of the transitions presented here have never been theoretically computed previously [(3)(pi-->pi(*)) and (3)(sigma-->pi(*)) adiabatic transitions in acetaldehyde and acetone] or have been studied only using moderate level (single reference based) ab initio methods (all adiabatic transitions in acetaldehyde). In the present work a consistent disagreement between NEVPT2 and experiment has been found for the (3)(pi-->pi(*)) adiabatic transition in all molecules: this result is attributed to the low intensity of the transition to the first vibrational levels of the excited state. The n-->pi(*) singlet and triplet vertical transition energies are also reported for all the molecules.     

Calculation of electric dipole transition moments using quasi-degenerate variational perturbation theory and averaged coupled-pair functional theory

Results are reported from calculations of electric dipole transition moments for various electronic transitions in Be, CH₂, and A1H using multireference singles and doubles configuration interaction, quasi-degenerate variational perturbation theory, and multireference averaged coupled pair functional theory. A simple normalization scheme is used for the quasi-degenerate variational perturbation theory and multireference averaged coupled pair functional theory wave functions. In all cases, comparison is made with full configuration interaction results in the valence space. For Be and CH₂, all methods are of comparable quality in calculating the transition moments and excitation energies, with averaged coupled-pair functional theory yielding slightly quicker convergence of the excitation energies and transition moments in most cases. For AlH, multireference singles and doubles configuration interaction is somewhat more accurate for the calculation of the transition moment. Factors that affect the accuracy of the methods are discussed. © 1994 John Wiley & Sons, Inc.     

Third-order multireference perturbation theory: the n-electron valence state perturbation-theory approach

A formulation of the n-electron valence state perturbation theory (NEVPT) at the third order of perturbation is presented. The present implementation concerns the so-called strongly contracted variant of NEVPT, where only a subspace of the first-order interacting space is taken into account. The resulting strongly contracted NEVPT3 approach is discussed in three test cases: (a) the energy difference between the 3B1 and 1A1 states of the methylene molecule, (b) the potential-energy curve of the N2 molecule ground state, and (c) the chromium dimer (Cr2) ground-state potential-energy profile. Particular attention is devoted to the last case where large basis sets comprising also h orbitals are adopted and where remarkable differences between the second- and third-order results show up.     

MRCI potential energy curves and spectroscopic constants of the ground and low-lying excited states of HgCd

The multireference configuration interaction (MRCI) electronic energy calculations with different basis sets have been performed on the ground state (X¹Σ) and three low-lying excited states (³Σ, ¹Π and ³Π) of HgCd dimer. The obtained potential energy curves (PECs) are fit to analytical potential energy functions (APEFs) using the Murrell–Sorbie potential function. Spectroscopic constants are calculated using the APEFs. Based on the PECs, the vibrational levels of each state are predicted. Our equilibrium positions of the X¹Σ state and ³Π state are in excellent agreement with the experimental reports.     

Quasirelativistic valence ab initio calculation of the potential-energy curves for Cd–rare gas atom pairs

The results of large-scale valence ab initio calculations of the potential-energy curves for the ground states and several excited states of Cd–rare gas (RG) van der Waals molecules are reported. In the calculations, Cd²⁰⁺ and RG⁸⁺ cores are simulated by energy-consistent pseudopotentials, which also account for scalar-relativistic effects and spin-orbit interaction within the valence shell. The potential energies of the Cd–RG species in the ΛS coupling scheme have been evaluated by means of ab initio complete-active-space multiconfiguration self-consistent-field (CASSCF)/CAS multireference second-order perturbation theory (CASPT2) calculations with a total 28 valence electrons, but the spin-orbit matrix has been computed in a reduced configuration interaction space restricted to the CASSCF level. Finally, the Ω potential curves are obtained by diagonalization of the modified spin-orbit matrix (its diagonal elements before diagonalization substituted by the corresponding CASPT2 eigenenergies). The calculated potential curves, especially the spectroscopic parameters derived for the ground states and several excited states of the Cd–RG species are presented and discussed in the context of available experimental data. The theoretical results exhibit very good agreement with experiment. Received: 20 April 2000 / Accepted: 1 September 2000 / Published online: 21 December 2000     

Comparison of low-order multireference many-body perturbation theories

Tests have been made to benchmark and assess the relative accuracies of low-order multireference perturbation theories as compared to coupled cluster (CC) and full configuration interaction (FCI) methods. Test calculations include the ground and some excited states of the Be, H(2), BeH(2), CH(2), and SiH(2) systems. Comparisons with FCI and CC calculations show that in most cases the effective valence shell Hamiltonian (H(v)) method is more accurate than other low-order multireference perturbation theories, although none of the perturbative methods is as accurate as the CC approximations. We also briefly discuss some of the basic differences among the multireference perturbation theories considered in this work.     

Augmented Gaussian basis sets of double and triple zeta valence qualities for the atoms K and Sc–Kr: Applications in HF, MP2, and DFT calculations of molecular electric properties

Augmented Gaussian basis sets of double and triple zeta valence qualities plus polarization functions for the atoms K and from Sc to Kr are presented. They were generated from the all-electron unaugmented sets by addition of diffuse functions (s, p, d, f, and g symmetries) that were optimized for the anion ground states. From these sets, Hartree–Fock, second-order Møller–Plesset perturbation theory, and density functional theory electric dipole moment and dipole polarizability calculations for a sample of molecules were carried out. Comparison with theoretical and experimental values available in the literature was done.     

A convenient decontraction procedure of internally contracted state-specific multireference algorithms

Internally contracted state-specific multireference (MR) algorithms, either perturbative such as CASPT2 or NEVPT2, or nonperturbative such as contracted MR configuration interaction or MR coupled cluster, are computationally efficient but they may suffer from the internal contraction of the wave function in the reference space. The use of a low dimensional multistate model space only offers limited flexibility and is not always practicable. The present paper suggests a convenient state-specific procedure to decontract the reference part of the wave function from a series of state-specific calculations using slightly perturbed zero-order wave functions. The method provides an orthogonal valence bond reading of the ground state and an effective valence Hamiltonian, the excited roots of which are shown to be relevant. The orthogonal valence bond functions can be considered quasidiabatic states and the effective valence Hamiltonian gives therefore the quasidiabatic energies and the electronic coupling among the quasidiabatic states. The efficiency of the method is illustrated in two case problems where the dynamical correlation plays a crucial role, namely, the LiF neutral/ionic avoided crossing and the F(2) ground state wave function.     

Applicability of multireference many-body perturbation theory to the Ne2+ molecule

The ground state as well as some low-lying excited states of the Ne₂⁺ molecule are calculated by means of the third-order multireference many-body perturbation theory with the “full” eight-orbital valence space using DZP and polarized valence TZ basis sets. The problem encountered with a large number of valence electrons is avoided by a proper definition of the Fermi vacuum. The calculated equilibrium distance of 1.721 Å and chemical dissociation energy D₀ = 1.283 eV are in good agreement with experimental results. A comparison with other ab initio techniques is also provided. © 1997 John Wiley & Sons, Inc.