State-specific Multireference Perturbation Theory Research Articles

Exploration of interlacing and avoided crossings in a manifold of potential energy curves by a unitary group adapted state specific multi-reference perturbation theory (UGA-SSMRPT).

The Unitary Group Adapted State-Specific Multi-Reference Perturbation Theory (UGA-SSMRPT2) developed by Mukherjee et al. [J. Comput. Chem. 36, 670 (2015)] has successfully realized the goal of studying bond dissociation in a numerically stable, spin-preserving, and size-consistent manner. We explore and analyze here the efficacy of the UGA-SSMRPT2 theory in the description of the avoided crossings and interlacings between a manifold of potential energy curves for states belonging to the same space-spin symmetry. Three different aspects of UGA-SSMRPT2 have been studied: (a) We introduce and develop the most rigorous version of UGA-SSMRPT2 that emerges from the rigorous version of UGA-SSMRCC utilizing a linearly independent virtual manifold; we call this the "projection" version of UGA-SSMRPT2 (UGA-SSMRPT2 scheme P). We compare and contrast this approach with our earlier formulation that used extra sufficiency conditions via amplitude equations (UGA-SSMRPT2 scheme A). (b) We present the results for a variety of electronic states of a set of molecules, which display the striking accuracy of both the two versions of UGA-SSMRPT2 with respect to three different situations involving weakly avoided crossings, moderate/strongly avoided crossings, and interlacing in a manifold of potential energy curves (PECs) of the same symmetry. Accuracy of our results has been benchmarked against IC-MRCISD + Q.

Single-Root Multireference Brillouin-Wigner Perturbative Approach to Excitation Energies.

The state-specific Brillouin–Wigner multireference perturbation theory [which employs Jeziorski–Monkhorst parametrization of the wave function] using improved virtual orbitals, denoted as IVO-BWMRPT, is applied to calculate excitation energies (EEs) for methylene, ethylene, trimethylenemethane, and benzyne systems exhibiting various degrees of diradical character. In IVO-BWMRPT, all of the parameters appearing in the wave function ansatz are optimized for a specific electronic state. For these systems, the IVO-BWMRPT method provides EEs that are in close agreement with the benchmark results and experiments, where available, indicating that the method does not introduce imbalance in the target-specific treatment of closed- and open-shell states involved. The good performance of the present methodology is primarily related to structural compactness of the formalism. Overall, present findings are encouraging for both further development of the approach and chemical applications on the energy differences of strongly correlated systems.

Taming the excited states of butadiene, hexatriene, and octatetraene using state specific multireference perturbation theory with density functional theory orbitals.

To compute the electronic excitation energies, a state-specific multireference Møller-Plesset perturbation theory (SSMRPT) with a complete active space configuration interaction reference function constructed using the orbitals obtained by the density functional theory (DFT) is presented as an accurate, as well as computationally affordable, and efficient protocol at the level of second order. The global hybrid B3LYP (Becke, 3-parameter, Lee-Yang-Parr) functional has been used to generate orbitals. The present method, called DFT-SSMRPT, uses perturbers that are individual Slater determinants and accounts for the coupling between the nondynamical and dynamical correlation effects. We have applied the new method to compute excitation energies in conjugated systems of π-electrons such as trans-1,3-butadiene, trans,trans-1,3,5-hexatriene, and all-trans-1,3,5,7-octatetraene. The ordering of the excited states is correctly reproduced by the DFT-SSMRPT calculations. The relative ordering of low-lying excited 1Bu and 1Ag states alters when the length of the polyene changes. The results match reasonably well with the literature including experimental and best theoretical findings. The accuracy of the method is sufficient to discern the energy gap between the close low-lying singlet and triplet states. The DFT-SSMRPT appears as an affordable computational ab initio avenue for a qualitatively correct description of excitation energies.

New benzene dimers: an MRMP2 study

The reaction energies of one cis-fused and four new trans-fused benzene dimers have been studied with state-specific multi-reference Moller-Plesset perturbation theory of the second order (MRMP2) based on reference CASSCF(12,12) wavefunctions. The cis-fused dimer 1, the product of symmetry-allowed [4 + 2] cycloaddition process, has been previously characterized experimentally and theoretically and, in this study, was used as reference. Dimer 1 lies 45 kcal/mol above two isolated benzene molecules, and its retro-dimerization activation energy is ~ 8 kcal/mol. In contrast, the [4 + 2] formation of trans-fused dimer 2 is symmetry-forbidden with an energetic driving force (Erel) of 57.6 kcal/mol. An activation barrier for corresponding retro-dimerization calculated to be 31.0 kcal/mol. The thermal [2 + 2] formation of dimers 3 and 4 are also symmetry-forbidden. They have been calculated to be 79.0 kcal/mol and 105.1 kcal/mol higher in energy than two isolated benzene molecules, respectively. However, the activation energies of 23.2 and 20.5 kcal/mol could allow for kinetic persistence of these compounds. Dimer 5 is the only symmetry-allowed [2 + 2] cycloaddition product. With Erel of 67.5 kcal/mol and Ea for retro-dimerization reaction of 19.2 kcal/mol, it shows high similarity with the symmetry-forbidden dimers. The wave function for each of the dimers at their local minimum geometry contains greater than 80% of the configuration $$\sigma^{4} \pi^{8} \sigma^{*0} \pi^{*0}$$. The transition state for the retro-dimerization of 1 (1TS) also contains more than 80% of the closed-shell configuration $$\sigma^{4} \pi^{8} \sigma^{*0} \pi^{*0}$$. For 2TS–5TS systems, the wavefunctions exhibit significant biradical character (20%, 20%, 14% and 26%, respectively).

A simplified account of the correlation effects to bond breaking processes: The Brillouin-Wigner perturbation theory using a multireference formulation

Adaptation of improved virtual orbital complete active space configuration interaction functions in state-specific multireference perturbation theory motivated by the Brillouin-Wigner perturbation scheme using Møller-Plesset multipartitioning is examined. The method, denoted as IVO-BWMRPT, focuses on only the root of principal interest at a time using single-root parameterization of Jeziorski-Monkhorst ansatz within the frame of an effective Hamiltonian. This approach yields size-extensive energy and avoids intruder-state problems in a natural manner. It allows relaxation of the reference space wave function in the presence of the perturbation which produces an important differential effect on the energy and cannot be neglected for quasidegenerate electronic states. The method has been tested against nontrivial situations such as the Be + H2 insertion profile along with the energy surfaces of FH and X2 (X = F, Cl, and Br), in which conventional single-reference methods generally fail, exhibiting very encouraging findings. We also consider the energy surfaces of ethylene (by breaking the π bond as well as the CC bond) and for the twisting of tetramethyleneethane. IVO-BWMRPT represents a rather balanced protocol for the description of molecules at a wide range of geometries, including stretched or dissociating bonds. Close agreement of our estimates with the reference values provides a useful measure for the success of the IVO-BWMRPT method to treat strongly correlated systems. Our results for TME show that the singlet state always lies below the triplet state for different conformations. The IVO-BWMRPT furnishes a compact and correct representation of the MR-wave function, and hence, a large variety of quasidegenerate situations can be accommodated within the method.

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.

Taming the Electronic Structure of Diradicals through the Window of Computationally Cost Effective Multireference Perturbation Theory.

Recently a state-specific multireference perturbation theory (SSMRPT) with an improved virtual orbitals complete active space configuration interaction (IVO-CASCI) reference function has been proposed for treating electronic structures of radicals such as methylene, m-benzyne, pyridyne, and pyridynium cation. This new development in MRPT, termed as IVO-SSMRPT, ensures that it is able to describe the structure of radicaloids with reasonable accuracy even with small reference spaces. IVO-SSMRPT is also capable of predicting the correct ordering of the lowest singlet-triplet gaps. Investigation of the first three electronic states of the oxygen molecule has also been used for rating our method. The agreement of our estimates with the available far more expensive benchmark state-of-the-art ab initio calculations is creditable. The IVO-SSMRPT method provides an effective avenue with manageable cost/accuracy ratio for accurately dealing with radicaloid systems possessing varying degrees of quasidegeneracy.

State‐specific multireference perturbation theory: development and present status

The state‐specific multireference perturbation theory (SSMRPT), which provides one state at a time may now gradually become a new useful ab initio tool for studying electronic states with strong configurational quasidegeneracy owing primarily to its suitability toward numerical implementation in the presence of intruders and also to a great extent for its firm theoretical construct and the scope of a systematic and hierarchical improvement. The method works with a complete active space, and treats each of the model space functions on the same footing by exploiting Jeziorski–Monkhorst parametrization of the wavefunction. The SSMRPT is size‐extensive and size‐consistent (with the orbitals localized). The real challenge remains in developing MRPT methods capable of maintaining explicit size‐extensivity and avoiding intruders over a vast range of molecular geometries. Recently developed relativistic SSMRPT for the four‐component spinors is very promising to describe the near‐degenerate states of molecules containing heavy atoms. The analysis of the formal aspects and practical utility of the SSMRPT method vis‐à‐vis the other MRPT formalisms that bear kinship with the SSMRPT formulation is also presented. Illustrative results show high accuracy of the SSMRPT method in describing quasidegenerate situations such as those appearing when one or more covalent bonds in the molecule become stretched or broken. While actively pursuing SSMRPT method, it became apparent to us that this method encounters two major limitations: (1) the scaling of the computational cost with respect to the number of active orbitals and (2) the lack of invariance of the energy with respect to a unitary transformation of the active orbitals. The future will tell whether the SSMRPT method will be able to acquire the same faith as other widely used single‐root MRPT methods. WIREs Comput Mol Sci 2016, 6:266–291. doi: 10.1002/wcms.1248This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods

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.

State-specific multireference perturbation theory with improved virtual orbitals: taming the ground state of F2 , Be2, and N2.

Adaptation of improved virtual orbitals (IVOs) in state-specific multireference perturbation theory using Møller-Plesset multipartitioning of the Hamiltonian (IVO-SSMRPT) is examined in which the IVO-complete active space configuration interaction (CASCI) is used as an inexpensive alternative to the more involved CAS-self-consistent field (CASSCF) orbitals. Unlike the CASSCF approach, IVO-CASCI does not bear tedious and costly iterations beyond those in the initial SCF calculation. The IVO-SSMRPT is intruder-free, and explicitly size-extensive. In the present preliminary study, the IVO-SSMRPT method which relies on a small reference space is applied to study potential energy surfaces (PES) of the ground state of challenging, multiconfigurational F2 , Be2 , and N2 molecules. These systems provide a serious challenge to any ab initio methodology due to the presence of an intricate interplay of nondynamical and dynamical correlations to the entire PES. The quality of the computed PES has been judged by extracting spectroscopic parameters and vibrational levels. The reported results illustrate that the IVO-SSMRPT method has a potential to yield accuracies as good as the CASSCF-SSMRPT one with reduced computational labor. Even with small reference spaces, our estimates demonstrate a good agreement with the available experimental values, and some benchmark computations. The blend of accuracy and low computational cost of IVO-SSMRPT should deserve future attention for the accurate treatment of electronic states of small to large molecular systems for which the wavefunction is characterized by various configurations.

Unitary group adapted state specific multireference perturbation theory: Formulation and pilot applications.

We present here a comprehensive account of the formulation and pilot applications of the second-order perturbative analogue of the recently proposed unitary group adapted state-specific multireference coupled cluster theory (UGA-SSMRCC), which we call as the UGA-SSMRPT2. We also discuss the essential similarities and differences between the UGA-SSMRPT2 and the allied SA-SSMRPT2. Our theory, like its parent UGA-SSMRCC formalism, is size-extensive. However, because of the noninvariance of the theory with respect to the transformation among the active orbitals, it requires the use of localized orbitals to ensure size-consistency. We have demonstrated the performance of the formalism with a set of pilot applications, exploring (a) the accuracy of the potential energy surface (PES) of a set of small prototypical difficult molecules in their various low-lying states, using natural, pseudocanonical and localized orbitals and compared the respective nonparallelity errors (NPE) and the mean average deviations (MAD) vis-a-vis the full CI results with the same basis; (b) the efficacy of localized active orbitals to ensure and demonstrate manifest size-consistency with respect to fragmentation. We found that natural orbitals lead to the best overall PES, as evidenced by the NPE and MAD values. The MRMP2 results for individual states and of the MCQDPT2 for multiple states displaying avoided curve crossings are uniformly poorer as compared with the UGA-SSMRPT2 results. The striking aspect of the size-consistency check is the complete insensitivity of the sum of fragment energies with given fragment spin-multiplicities, which are obtained as the asymptotic limit of super-molecules with different coupled spins.

Spin-adaptation and redundancy in state-specific multireference perturbation theory

Spin-adaptation of virtual functions in state-specific multireference perturbation theory is examined. Redundancy occurring among virtual functions generated by unitary group based excitation operators on a model-space function is handled by canonical orthogonalization. The treatment is found to remove non-physical kinks observed earlier on potential energy surfaces. Sensitivity analysis of the new approach confirms the elimination of the drastic increase in singular values of sensitivity matrices, reported earlier.

Publisher's Note: “A spin-adapted size-extensive state-specific multi-reference perturbation theory. I. Formal developments” [J. Chem. Phys. 136, 024105 (2012)

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A spin-adapted size-extensive state-specific multi-reference perturbation theory with various partitioning schemes. II. Molecular applications

Following the theoretical development of a spin-adapted state-specific multi-reference second-order perturbation theory (SA-SSMRPT2) as expounded in the preceding publication, we discuss here its implementation and the results of its applications to potential energy curves (PECs) of various electronic states of small molecules. In particular, we illustrate its efficacy in states of various spin multiplicities and varying multi-reference character. Both Møller-Plesset (MP) and Epstein-Nesbet (EN) type of partitions have been explored. Also, a straightforward Rayleigh-Schrödinger (RS) and Brillouin-Wigner (BW) version of the SA-SSMRPT2 have been studied. Ground state PECs were computed for singlet states of HF, BH, and H(2)O molecules as well as the doublet state of NH(2) and BeH radicals and compared to corresponding full configuration interaction numbers, which serve as benchmark results. As an extensive application on a production level, the ground state PECs of N(2), a classic example of multiple-bond breaking, were calculated using cc-pVXZ (X = 3,4,5) basis and then extrapolated to obtain estimates of the complete basis set limit. Vibrational energy levels were extracted from these N(2) PECs, which compare favorably to the experimental values. In addition, extensive studies were also carried out on PECs of the seven low-lying excited states of the N(2) molecule. Finally, it is shown that the flexibility to relax configuration coefficients in SA-SSMRPT2 helps to provide good descriptions for the avoided crossing between the two lowest (1)Σ states of the LiF molecule. Our results indicate (1) that more studies are needed to draw firm conclusions about the relative efficacies of the MP and EN results and (2) that the RS version works so well as compared to the BW version that the extra computational expenses needed in the later formalism is not warranted.

A spin-adapted size-extensive state-specific multi-reference perturbation theory. I. Formal developments

We present in this paper a comprehensive formulation of a spin-adapted size-extensive state-specific multi-reference second-order perturbation theory (SA-SSMRPT2) as a tool for applications to molecular states of arbitrary complexity and generality. The perturbative theory emerges in the development as a result of a physically appealing quasi-linearization of a rigorously size-extensive state-specific multi-reference coupled cluster (SSMRCC) formalism [U. S. Mahapatra, B. Datta, and D. Mukherjee, J. Chem. Phys. 110, 6171 (1999)]. The formulation is intruder-free as long as the state-energy is energetically well-separated from the virtual functions. SA-SSMRPT2 works with a complete active space (CAS), and treats each of the model space functions on the same footing. This thus has the twin advantages of being capable of handling varying degrees of quasi-degeneracy and of ensuring size-extensivity. This strategy is attractive in terms of the applicability to bigger systems. A very desirable property of the parent SSMRCC theory is the explicit maintenance of size-extensivity under a variety of approximations of the working equations. We show how to generate both the Rayleigh-Schrödinger (RS) and the Brillouin-Wigner (BW) versions of SA-SSMRPT2. Unlike the traditional naive formulations, both the RS and the BW variants are manifestly size-extensive and both share the avoidance of intruders in the same manner as the parent SSMRCC. We discuss the various features of the RS as well as the BW version using several partitioning strategies of the hamiltonian. Unlike the other CAS based MRPTs, the SA-SSMRPT2 is intrinsically flexible in the sense that it is constructed in a manner that it can relax the coefficients of the reference function, or keep the coefficients frozen if we so desire. We delineate the issues pertaining to the spin-adaptation of the working equations of the SA-SSMRPT2, starting from SSMRCC, which would allow us to incorporate essentially any type open-shell configuration-state functions (CSF) within the CAS. The formalisms presented here will be applied extensively in a companion paper to assess their efficacy.

Sensitivity analysis of state-specific multireference perturbation theory

State-specific multireference perturbation theory (SS-MRPT) developed by Mukherjee et al. [Int. J. Mol. Sci. 3, 733 (2002)] is examined focusing on the dependence of the perturbed energy on the initial model space coefficients. It has been observed earlier, that non-physical kinks may appear on the potential energy surface obtained by SS-MRPT while related coupled-cluster methods may face convergence difficulties. Though exclusion or damping of the division by small coefficients may alleviate the problem, it is demonstrated here that the effect does not originate in an ill-defined division. It is shown that non-negligible model space coefficients may also be linked with the problem. Sensitivity analysis is suggested as a tool for detecting the coefficient responsible. By monitoring the singular values of sensitivity matrices, orders of magnitude increase is found in the largest value, in the vicinity of the problematic geometry point on the potential energy surface. The drastic increase of coefficient sensitivities is found to be linked with a degeneracy of the target root of the effective Hamiltonian. The nature of the one-electron orbitals has a profound influence on the picture: a rotation among active orbitals may screen or worsen the effect.

Study of the Ground State Dissociation of Diatomic Molecular Systems Using State-Specific Multireference Perturbation Theory: A Brillouin-Wigner Scheme.

The size-extensive second-order state-specific (or single root) multireference (MR) perturbation theory (SS-MRPT) in the Brillouin-Wigner (BW) form using Mϕller-Plesset perturbative evaluations of orders up to 2 [termed as SS-MRMPPT(BW)] presents a viable, as well as promising, approach to include both nondynamic and dynamic correlations in the study of the bond-stretching (in multireference/quasidegenerate situations) of molecular species with a manageable cost/accuracy ratio. It combines numerical stability in the presence of an intruder state problem with strict size consistency (when localized orbitals are used). In this paper, the SS-MRMPPT(BW) method has been shown to properly break the bonds (in the ground state) of several diatomic molecules (such as F2, Cl2 and Br2, and BH) that have posed a severe challenge to any many-body theoretical approach due to the presence of quasidegeneracy of varying degrees in the ground state. A comparison of the resulting potentials with the various theoretical results reveals that the method represents a valuable tool that is capable of properly accounting even for very strong quasidegeneracies, while also performing well in nondegenerate situations. In this work, we have also calculated spectroscopic constants (such as equilibrium bond lengths, vibrational frequencies, and dissociation energies) of the ground state of these molecular systems. The SS-MRMPPT spectroscopic constants are compared with the most accurate available ab initio calculations and other theoretical estimates of previous works to calibrate the efficacy of the method. For the sake of completeness, we also compare the computed spectroscopic constants with the experimental observations. The accuracy of computed spectroscopic parameters appears to be rather consistent over a multitude of systems for various basis sets. The SS-MRMPPT enables quantitatively accurate and computationally affordable analysis of potential energy surfaces and spectroscopic constants of various multireference systems in the ground state. It is particularly visible for spectroscopic parameters and nonparallelism error (NPE) calculations. The calculations further reveal that the SS-MRMPPT(BW) method compared to its Rayleigh-Schrödinger counterpart [SS-MRMPPT(RS)] provides a more accurate and consistent solution for the whole dissociation path and spectroscopic constants.

Investigation of Low-Lying States of Oxygen Molecule via Second-Order Multireference Perturbation Theory: A State-Specific Approach

The relative performance of four variants of the Møller-Plesset (MP) partitioning (using different diagonal one-electron unperturbed Hamiltonian, H0) based state-specific multireference perturbation theory (SS-MRPT) [termed as SS-MRPT(MP)] has been investigated and demonstrated by calculations of the dissociation potential energy curves (PECs) of the first three electronic states [ground state X3Sigmag- as well as low-lying singlet excited states, a1Deltag and b1Sigmag+] of the oxygen molecule using different basis sets. The spectroscopic constants extracted from the computed PECs obtained by the SS-MRPT(MP) method are calibrated with respect to the corresponding value of the full configuration interaction (FCI) and experimental data for the corresponding states. We have also computed vertical excitation (or transition) energies and compared those with the corresponding FCI values along with the results of other available sophisticated methods. Encouraging agreement between SS-MRPT(MP) theory and some benchmark calculations has been observed. We have thus assessed the applicability and accuracy of the SS-MRPT(MP) method with different diagonal one-electron partitioning schemes. The ability of the SS-MRPT(MP) method with different partitioning schemes to predict full PECs and spectroscopic constants of the ground state and excited states with almost equivalent accuracy is promising.