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.

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.

Reappraisal of nuclear quadrupole moments of atomic halogens via relativistic coupled cluster linear response theory for the ionization process.

The coupled cluster based linear response theory (CCLRT) with four-component relativistic spinors is employed to compute the electric field gradients (EFG) of (35)Cl, (79)Br, and (127)I nuclei. The EFGs resulting from these calculations are combined with experimental nuclear quadrupole coupling constants (NQCC) to determine the nuclear quadrupole moments (NQM), Q of the halide nuclei. Our estimated NQMs [(35)Cl = -81.12 mb, (79)Br = 307.98 mb, and (127)I = -688.22 mb] agree well with the new atomic values [(35)Cl = -81.1(1.2), (79)Br = 302(5), and (127)I = -680(10) mb] obtained via Fock space multireference coupled cluster method with the Dirac-Coulomb-Breit Hamiltonian. Although our estimated Q((79)Br) value deviates from the accepted reference value of 313(3) mb, it agrees well with the recently recommended value, Q((79)Br) = 308.7(20) mb. Good agreement with current reference data indicates the accuracy of the proposed value for these halogen nuclei and lends credence to the results obtained via CCLRT approach. The electron affinities yielded by this method with no extra cost are also in good agreement with experimental values, which bolster our belief that the NQMs values for halogen nuclei derived here are reliable.

Taming the electronic structure of lead and eka-lead (flerovium) by the relativistic coupled cluster method.

Theoretical investigations of the superheavy elements (SHEs) are extremely challenging and are often the sole source of useful chemical information. Relativistic Fock-space multireference coupled cluster (RFS-MRCC) computations have been carried out for evaluating the ionization potential (IP), excitation energies (EE), nuclear magnetic hyperfine constant (A), lifetime (τ), and Landé g factor of singly ionized eka-lead (Fl II). To judge the accuracy of Fl II results, similar calculations are performed for Pb II, which shows a nice and consistent agreement with known experimental values. Thus, we believe that our predictions for Fl are reliable and useful for the simulation of experimental behavior. To the best of our knowledge, no prior theoretical and/or experimental information is available for A, τ, and g-factor of this SHE. The higher IPs and EEs of Fl II, with respect to Pb II, indicate the former to be more inert and less metallic than Pb. This is contingent on the effects of the relativistic stabilization of the 7s and 7p1/2 orbitals. The present analysis demonstrates the influence of higher-body cluster operators on atomic properties. The close agreement with the experiment (having an estimated error within 1-2%) indicates that the FS-MRCC method is a reliable predictive tool in cases where the experimental results are not readily available, such as the SHEs. The remaining source of error possibly stems out from the omission of the full-blown triple virtual excitations and the absence of Breit interaction.

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.

Diagnosis of the performance of the state-specific multireference coupled-cluster method with different truncation schemes.

We have tested the linked version of a iterative (partial) triples correction for the Jeziorski-Monkhorst ansatz based state-specific multireference coupled cluster (SS-MRCC) approach with singles and doubles (SD) excitations [abbreviated as SS-MRCCSDT-1a and SS-MRCCSDT-1a+d]. The assessments of SS-MRCCSDT-1a and SS-MRCCSDT-1a+d schemes have been performed on the ground potential energy surface (PES) of P4, Li(2),Be(2) systems which demand the MR description, and on study of the excitation energy between the ground and first excited state for P4 system. Illustrations in the isomerization of cyclobutadiene also show the power of the schemes. One of the designed features of the SS-MRCCSDT-n methods introduced here is that they do not require storage of the triples amplitudes. In the entire range of geometries, we found a definite improvement provided by SS-MRCC with SDT-1a and SDT-1a+d schemes over the standard SD one. In the nondegenerate regions of PES, the closeness of the performance of the single-reference CC to the SS-MRCC methods increases after inclusion of even partial triple excitations. Generally, the performance of the SS-MRCCSDT-1a+d approach is closer to the corresponding full configuration interaction (FCI) one than to the SS-MRCCSDT-1a specially in the degenerate geometries (as is evident from nonparallelism error). The deviation from FCI for the first excited state of the P4 model using various SS-MRCC theories with different truncation schemes obtained by converging on the second root of the effective Hamiltonian has also been reported. We also compare our results with the current generation state-of-the-art single and multireference CC calculations to envisage the usefulness of the present approach. Initial implementation indicates that the SS-MRCCSDT-n formalism can provide not only reliable excitation energies and barrier height even when used in a relatively small model space, but also offers a considerable promise in generating the entire energy surface with low nonparallelity error.

Second-order state-specific multireference Møller Plesset perturbation theory: Application to energy surfaces of diimide, ethylene, butadiene, and cyclobutadiene.

The complete active space spin-free state-specific multireference Møller-Plesset perturbation theory (SS-MRMPPT) based on the Rayleigh-Schrödinger expansion has proved to be very successful in describing electronic states of model and real molecular systems with predictive accuracy. The SS-MRMPPT method (which deals with one state while using a multiconfigurational reference wave function) is designed to avoid intruder effects along with a balanced description of both dynamic and static correlations in a size-extensive manner, which allows us to produce accurate potential energy surfaces (PESs) with a correct shape in bond-breaking processes. The SS-MRMPPT method is size consistent when localized orbitals on each fragment are used. The intruder state(s) almost inevitably interfere when computing the PESs involving the breaking of genuine chemical bonds. In such situations, the traditional effective Hamiltonian formalism often goes down, so that no physically acceptable solution can be obtained. In this work, we continue our analysis of the SS-MRMPPT method for systems and phenomena that cannot be described either with the conventional single-reference approach or effective Hamiltonian-based traditional MR methods. In this article, we investigate whether the encouraging results we have obtained at the SS-MRMPPT level in the study of cis-trans isomerization of diimide (N2H2), ethylene (C2H4), and 1,3-butadiene (C4H6) carry over to the study of chemical reactions. The energy surfaces of the double-bond flipping interconversion of the two equivalent ground and two lowest singlet state structures of cyclobutadiene have also been studied. All results have been discussed and assessed by comparing with other state-of-the-art calculations and corresponding experimental data whenever available.

Ab initio multireference investigation of disjoint diradicals: singlet versus triplet ground states.

We present improved virtual orbital (IVO) complete active space (CAS) configuration interaction (IVO-CASCI) and IVO-CASCI-based multireference Møller-Plesset perturbation theory (MRMPPT) calculations with an aim to elucidate the electronic structure of tetramethyleneethane (TME) in its lowest singlet and triplet state and to quantify their order and extent of splitting. The potential surfaces of singlet and triplet states for the twisting of TME are also studied. We found that the triplet state is higher in energy than the singlet one in the whole range of twisting angles with the energy gap minimum at a twisting angle of about 45°. Harmonic vibrational frequencies of TME have also been calculated for both the states. We also report the ground to first excited triplet state transition energies. Our results are analyzed with respect to the results available in the literature to illustrate the efficacy of our methods employed. We also demonstrate that the spin character of the ground state of disjoint, TME-like diradicals can be manipulated by using appropriate selection of annulenic spacer to separate the allyl groups of TME.

Evaluation of the performance of single root multireference coupled cluster method for ground and excited states, and its application to geometry optimization.

The complete model space (CAS) based "genuine" single root multireference (MR) coupled cluster (sr-MRCC) method [Mahapatra and Chattopadhyay, J. Chem. Phys. 133, 074102 (2010)] has been extended to enable geometry optimizations by adopting the numerical gradient scheme. The sr-MRCC theory is designed to treat quasidegeneracies of varying degrees through the computation of essential static and dynamic correlation effects in a balanced way while bypassing the intruder states problem in a size-extensive manner. The efficacy of our sr-MRCC gradient approach has been illustrated by the optimization of the geometries of N(2)H(2),CH(2),C(2)H(4),C(4)H(4),O(3) as well as trimethylenemethane (TMM) molecular systems, since such cases, by virtue of their complexity, warrant truly multireference description. We have explored the capability of the sr-MRCC approach to yield rotational energy surfaces for the ground and first singlet excited states of N(2)H(2). We also intend to explore the ground and the excited state energetics of some model systems (such as P4, H4, and H(8)) for the computation of excitation energies by relying on the sr-MRCC method. An analysis of the results and a comparison with previous pertinent theoretical works including state specific MRCC (SS-MRCC) theory of Mukherjee and co-workers have also been presented. Although in most of the cases, we observe a close behavior between the sr-MRCC and SS-MRCC method, the error in the sr-MRCC is lower than the overall error of the SS-MRCC calculations in the vicinity of the transition region (manifesting a significant quasidegenerate character). The present results show that the sr-MRCC method and its numerical gradient variant are generally applicable to very demanding model and realistic chemical problems at acceptable accuracy and affordable computational expense which together attests the efficacy and viability of the sr-MRCC formalism for handling of static and dynamic correlations simultaneously thereby ensuring a balanced description for bond-breaking and other quasidegenerate situations with a various degree of MR character. Our preliminary results illustrate that our sr-MRCC method is a potential competitor for other state specific MRCC theories.

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.

Second-order state-specific multireference Møller-Plesset perturbation theory (SS-MRMPPT) applied to geometry optimization.

The performance of a numerically oriented gradient scheme for the previously introduced second-order state-specific multireference Møller-Plesset perturbation theory (SS-MRMPPT) has been tested to compute certain geometrical parameters (such as bond lengths and angles). Various examples [H2O, O3, N2H2, C2H4, C2H2F2, 1,3-butadiene (C4H6), cyclobutadiene (C4H4), and 2,6-pyridynium cation (C5NH4(+))] have been presented to validate the implementation of the SS-MRMPPT gradient approach. To illustrate the reliability of our findings, comparisons have been made with the previously reported theoretical results. The accuracy of our calculations has further been assessed by comparing with the experimental results whenever available. On the basis of the present work, we arrive at the conclusion that the SS-MRMPPT gradient scheme has substantial potential in computing the geometrical parameters for several rather diverse molecular systems, whether charged or neutral and having the closed-shell ground state or being open-shell radicals or biradicals or strongly perturbed by intruders. It is worthwhile to emphasize that the present work represents the first systematic application of the SS-MRMPPT numerical gradient approach.

Potential energy surface studies via a single root multireference coupled cluster theory.

We have employed complete active space based single root multireference coupled cluster method (the resulting method is referred to by the acronym sr-MRCC) to compute the potential energy surfaces (PESs) of some well studied "protypical model" systems for which a highly accurate and reliable database is available for comparison. As that of state-specific theory, the sr-MRCC approach focuses and correlates one state while using a multiconfigurational reference and thus it naturally avoids intruder states. The present method is structurally different from the well known state specific multireference coupled cluster (SS-MRCC) method introduced by Mahapatra et al. [Mol. Phys. 94, 157 (1998)]. As that of the SS-MRCC theory, the present method is also based on the Jeziorski-Monkhorst ansatz where a different exponential cluster operator exp(T(mu)) acts on its corresponding model function phi(mu). The final cluster finding equations contain coupling between the cluster operators for all the mu, which are mainly responsible to prove the extensivity of both the cluster amplitudes and the energy. The present sr-MRCC theory is size-extensive and size-consistent when localized orbitals are used. The systems considered here exhibit varying degrees of degeneracy at different regions of PES. The treatment of these systems via traditional effective Hamiltonian based methods suffers from divergence problems in the iterative solution of the CC equations (the issue termed as "intruder state"). The sr-MRCC results lie closer to the ones obtained by the SS-MRCC method for these systems. To judge the efficacy of the present method, we have compared our results with other previously published theoretical estimations, which clearly indicate that the present method is reliable in studying the dissociation PES of states plagued by electronic degeneracy as well as notorious intruder effects. The highly satisfactory performance of the sr-MRCC method, vis-a-vis the other sophisticated methods, in describing the lowest and the first excited singlet states of BeH(2) at points of high degeneracy is noticeable.

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.

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.

Application of state-specific multireference Møller-Plesset perturbation theory to nonsinglet states.

We present molecular applications of a spin free size-extensive state-specific multireference perturbation theory (SS-MRPT), which is valid for model functions of arbitrary spin and generality. In addition to the singlet states, this method is equally capable to handle nonsinglet states. The formulation based on Rayleigh-Schrodinger approach works with a complete active space and treats each of the model space functions democratically. The method is capable of handling varying degrees of quasidegeneracy and of ensuring size consistency as a consequence of size extensivity. In this paper, we illustrate the effectiveness of the Møller-Plesset (MP) partitioning based spin free SS-MRPT [termed as SS-MRPT(MP)] in computations of energetics of the nonsinglet states of several chemically interesting and demanding molecular examples such as LiH, NH(2), and CH(3). The spectroscopic constants of (3)Sigma(-) state of NH and OH(+) molecular systems and the ground (1)Sigma(g) (+) as well as excited (3)Sigma(u)(+) states of N(2) have been investigated and comparison with experimental and full configuration interaction values (wherever available) has also been provided. We have been able to demonstrate here that the SS-MRPT(MP) method is an intrinsically consistent and promising approach to compute reliable energies of nonsinglet states over different geometries.

Molecular applications of state-specific multireference perturbation theory to HF, H2O, H2S, C2, and N2 molecules.

In view of the initial success of the complete active space (CAS) based size-extensive state-specific multireference perturbation theory (SS-MRPT) [J. Phys. Chem. A 103, 1822 (1999)] for relatively diverse yet simple chemically interesting systems, in this paper, we present the computation of the potential energy curves (PEC) of systems with arbitrary complexity and generality such as HF, H(2)O, H(2)S, C(2), and N(2) molecules. The ground states of such systems (and also low-lying singlet excited states of C(2)) possess multireference character making the description of the state difficult with single-reference (SR) methods. In this paper, we have considered the Moller-Plesset (MP) partitioning scheme [SS-MRPT(MP)] method. The accuracy of energies generated via SS-MRPT(MP) method is tested through comparison with other available results. Comparison with FCI has also been provided wherever available. The accuracy of this method is also demonstrated through the calculations of NPE (nonparallelism error) and the computation of the spectroscopic constants of all the above mentioned systems. The quality of the computed spectroscopic constants is established through comparison with the corresponding experimental and FCI results. Our numerical investigations demonstrate that the SS-MRPT(MP) approach provides a balanced treatment of dynamical and non-dynamical correlations across the entire PECs of the systems considered.

Application of improved virtual orbital based multireference methods to N2, LiF, and C4H6 systems.

The improved virtual orbital (IVO) complete active space configuration interaction (CASCI) based multiconfigurational quasidegenerate perturbation theory (MCQDPT) and its single-root version (termed as MRMPPT) are applied to assess the efficacy and the reliability of these two methods. Applications involve the ground and/or excited state potential energy curves (PECs) of N(2), LiF, and C(4)H(6) (butadiene) molecules, systems that are sufficiently complex to assess the applicability of these methods. The ionic-neutral curve crossing involving the lowest two (1)Sigma(+) states of LiF molecule is studied using the IVO-MCQDPT method, while its single-root version (IVO-MRMPPT) is employed to study the ground state PEC for isomerization of butadiene and to model the bond dissociation of N(2) molecule. Comparisons with the standard methods (full CI, coupled cluster with singles and doubles, etc.) demonstrate that the IVO-based MRMPPT and MCQDPT approaches provide smooth and reliable PECs for all the systems studied. The IVO-CASCI method is explored to enable geometry optimization for ground state of C(4)H(6) using numerical energy gradients. The ground spectroscopic constants of N(2) and LiF determined using the numerical gradient based IVO-CASCI method are in accord with experiment and with other correlated calculations. As an illustration, we may point out that the maximum deviation from the experiment in our estimated normal mode frequency of LiF is 34 cm(-1), whereas for the bond length, the maximum error is just 0.012 A.

Reappraisal of cis effect in 1,2-dihaloethenes: an improved virtual orbital multireference approach.

Computed relative stabilities for isomers of 1,2-difluoroethene and 1,2-dichloroethene isomers are compared with predictions based on chemical hardness (eta) and electrophilicity (omega) using the principles of maximum hardness and minimum electrophilicity. The chemical hardness and electrophilicity deduced either from improved virtual orbital (IVO) energies or from correlated treatments correctly predict that cis 1,2-difluoroethene and 1,2-dichloroethene are energetically more stable than the corresponding trans isomers, and the ground state energies from multireference perturbation theory with IVO orbitals agree with these predictions. However, when the same quantities are computed using Hartree-Fock orbitals, serious inconsistencies between the two approaches emerge in predicting the stability of the isomers of the 1,2-dihaloethenes. The present study clearly demonstrates that the IVO energies are appropriate for the computation of hardness related parameters, notably the chemical hardness and electrophilicity. Moreover, the IVO methods also provide smooth potential energy curves for the cis-trans isomerization of the two 1,2-dihaloethenes.

A state-specific approach to multireference coupled electron-pair approximation like methods: development and applications.

The traditional multireference (MR) coupled-cluster (CC) methods based on the effective Hamiltonian are often beset by the problem of intruder states, and are not suitable for studying potential energy surface (PES) involving real or avoided curve crossing. State-specific MR-based approaches obviate this limitation. The state-specific MRCC (SS-MRCC) method developed some years ago can handle quasidegeneracy of varying degrees over a wide range of PES, including regions of real or avoided curve-crossing. Motivated by its success, we have suggested and explored in this paper a suite of physically motivated coupled electron-pair approximations (SS-MRCEPA) like methods, which are designed to capture the essential strength of the parent SS-MRCC method without significant sacrificing its accuracy. These SS-MRCEPA theories, like their CC counterparts, are based on complete active space, treat all the reference functions on the same footing and provide a description of potentially uniform precision of PES of states with varying MR character. The combining coefficients of the reference functions are self-consistently determined along with the cluster amplitudes themselves. The newly developed SS-MRCEPA methods are size-extensive, and are also size-consistent with localized orbitals. Among the various versions, there are two which are invariant with respect to the restricted rotations among doubly occupied and active orbitals separately. Similarity of performance of this latter and the noninvariant versions at the crossing points of the degenerate orbitals imply that the all the methods presented are rather robust with respect to the rotations among degenerate orbitals. Illustrative numerical applications are presented for PES of the ground state of a number of difficult test cases such as the model H4, H(8) problems, the insertion of Be into H(2), and Li(2), where intruders exist and for a state of a molecule such as CH(2), with pronounced MR character. Results obtained with SS-MRCEPA methods are found to be comparable in accuracy to the parent SS-MRCC and FCI/large scale CI results throughout the PES, which indicates the efficacy of our SS-MRCEPA methods over a wide range of geometries, despite their neglect of a host of complicated nonlinear terms, even when the traditional MR-based methods based on effective Hamiltonians fail due to intruders.