A systematic improvement to UGA-SSMRCCSD equations and its implication for potential energy curves.

The Unitary Group Adaptation (UGA) offers a very compact and efficient spin adaptation strategy for any spin-free Hamiltonian in a many body framework. Our use of UGA in the context of state-specific (SS) Jeziorski-Monkhorst Ansatz based multireference coupled cluster (MRCC) theory obviates the non-commutativity between the spin-free cluster operators via a normal ordered exponential parametrization in the wave operator. A previous formulation of UGA-SSMRCC by us [R.

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.

Unitary coupled-cluster based self-consistent polarization propagator theory: A third-order formulation and pilot applications.

In this article, the development of a third-order self-consistent polarization propagator method based on unitary coupled-cluster (UCC) parametrization of the ground-state wavefunction and the excitation manifold comprising unitary-transformed excitation operators, hereafter referred to as UCC3, is reported. The UCC3 method is designed to provide excitation energies correct up to the third order for excited states dominated by single excitations. An expansion for the UCC transformed Hamiltonian involving Bernoulli numbers as expansion coefficients is adopted in the derivation of UCC3 working equations.

Inclusion of orbital relaxation and correlation through the unitary group adapted open shell coupled cluster theory using non-relativistic and scalar relativistic Hamiltonians to study the core ionization potential of molecules containing light to medium-heavy elements.

The orbital relaxation attendant on ionization is particularly important for the core electron ionization potential (core IP) of molecules. The Unitary Group Adapted State Universal Coupled Cluster (UGA-SUMRCC) theory, recently formulated and implemented by Sen et al. [J.

4-Component relativistic calculations of L3 ionization and excitations for the isoelectronic species UO2(2+), OUN(+) and UN2.

We present a 4-component relativistic study of uranium 2p3/2 ionization and excitation in the isoelectronic series UO2(2+), OUN(+) and UN2. We calculate ionization energies by ΔSCF at the Hartree-Fock (HF) and Kohn-Sham (KS) level of theory. At the ΔHF level we observe a perfectly linear chemical shift of ionization energies with respect to uranium atomic charges obtained from projection analysis.

Aspects of Size-Consistency of Orbitally Noninvariant Size-Extensive Multireference Perturbation Theories: A Case Study Using UGA-SSMRPT2 as a Prototype.

Profiling a potential energy surface (PES), all the way to dissociate a molecular state into particular fragments and to display real or avoided crossings, requires a multireference description and the maintenance of size-consistency. The many body methods, which suit this purpose, should thus be size-extensive. Size-extensive theories, which are invariant with respect to transformation among active orbitals are, in principle, size-consistent.

Pattern of Drug Use and Associated Behaviors Among Female Injecting Drug Users From Northeast India: A Multi-Centric, Cross-Sectional, Comparative Study.

Background: Studies from developed countries document the presence of injecting drug use among females and significantly higher vulnerabilities and risks as compared with male injecting drug users (IDUs). Studies comparing vulnerabilities and drug use patterns between female and male IDUs are not available for developing countries.

Objectives: The aim of the study was to assess the drug use pattern and related HIV vulnerabilities among female IDUs and compare these findings with those from male IDUs from four states of Northeast India.

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.

Excited states with internally contracted multireference coupled-cluster linear response theory.

In this paper, the linear response (LR) theory for the variant of internally contracted multireference coupled cluster (ic-MRCC) theory described by Hanauer and Köhn [J. Chem. Phys.

Communication: Extension of a universal explicit electron correlation correction to general complete active spaces.

We present the extension of a recently proposed universal explicit electron correlation (F12) correction for multi-reference perturbation theories to general complete active spaces and arbitrary choices of complete active space self-consistent field (CASSCF) orbitals. This F12 correction is applied to Mukherjee's multi-reference second-order perturbation theory (Mk-MRPT2). Pilot examples show the expected reduction of the basis sets incompleteness error of about two cardinal numbers.

Exploration of Various Aspects of UGA-SUMRCC: Size Extensivity, Possible Use of Sufficiency Conditions, and an Extension for Direct Determination of Energy Differences.

The Unitary Group Adapted State Universal Multireference Coupled Cluster (UGA-SUMRCC) theory, recently developed by us (J. Chem. Phys.

Development and applications of a unitary group adapted state specific multi-reference coupled cluster theory with internally contracted treatment of inactive double excitations.

Any multi-reference coupled cluster (MRCC) development based on the Jeziorski-Monkhorst (JM) multi-exponential ansatz for the wave-operator Ω suffers from spin-contamination problem for non-singlet states. We have very recently proposed a spin-free unitary group adapted (UGA) analogue of the JM ansatz, where the cluster operators are defined in terms of spin-free unitary generators and a normal ordered, rather than ordinary, exponential parametrization of Ω is used. A consequence of the latter choice is the emergence of the "direct term" of the MRCC equations that terminates at exactly the quartic power of the cluster amplitudes.

Formulation and implementation of a unitary group adapted state universal multi-reference coupled cluster (UGA-SUMRCC) theory: excited and ionized state energies.

The traditional state universal multi-reference coupled cluster (SUMRCC) theory uses the Jeziorski-Monkhorst (JM) based Ansatz of the wave operator: Ω = Σ(μ)Ω(μ)|φ(μ)><φ(μ)|, where Ω(μ) = exp(T(μ)) is the cluster representation of the component of Ω inducing virtual excitations from the model function φ(μ). In the first formulations, φ(μ)s were chosen to be single determinants and T(μ)s were defined in terms of spinorbitals. This leads to spin-contamination for the non-singlet cases.

Unitary group adapted state-specific multi-reference coupled cluster theory: formulation and pilot numerical applications.

We present the formulation and the implementation of a spin-free state-specific multi-reference coupled cluster (SSMRCC) theory, realized via the unitary group adapted (UGA) approach, using a multi-exponential type of cluster expansion of the wave-operator Ω. The cluster operators are defined in terms of spin-free unitary generators, and normal ordered exponential parametrization is utilized for cluster expansion instead of pure exponentials. Our Ansatz for Ω is a natural spin-free extension of the spinorbital based Jeziorski-Monkhorst (JM) Ansatz.

Inactive excitations in Mukherjee's state-specific multireference coupled cluster theory treated with internal contraction: development and applications.

One generic difficulty of most state-specific many-body formalisms using the Jeziorski-Monkhorst ansatz: ψ = Σ(μ)exp(T(μ))|φ(μ)>c(μ) for the wave-operators is the large number of redundant cluster amplitudes. The number of cluster amplitudes up to a given rank is many more in number compared to the dimension of the Hilbert Space spanned by the virtual functions of up to the same rank of excitations. At the same time, all inactive excitations--though linearly independent--are far too numerous.

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.

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.

The spin-free analogue of Mukherjee's state-specific multireference coupled cluster theory.

In this paper, we develop a rigorously spin-adapted version of Mukherjee's state-specific multireference coupled cluster theory (SS-MRCC, also known as Mk-MRCC) [U. S. Mahapatra, B.

Inclusion of selected higher excitations involving active orbitals in the state-specific multireference coupled-cluster theory.

The parent state-specific multireference coupled-cluster (SS-MRCC) theory proposed by Mukherjee et al. [J. Chem.

An algebraic proof of generalized Wick theorem.

The multireference normal order theory, introduced by Kutzelnigg and Mukherjee [J. Chem. Phys.

Full implementation and benchmark studies of Mukherjee's state-specific multireference coupled-cluster ansatz.

The state-specific multireference coupled-cluster (SS-MRCC) ansatz developed by Mukherjee and co-workers [J. Chem. Phys.

Comparative study of multireference perturbative theories for ground and excited states.

Three recently developed multireference perturbation theories (PTs)-generalized Van Vleck PT (GVVPT), state-specific multireference PT (SS-MRPT), and multiconfiguration PT (MCPT)-are briefly reviewed and compared numerically on representative examples, at the second order of approximations. We compute the dissociation potential curve of the LiH molecule and the BeH(2) system at various geometries, both in the ground and in the first excited singlet state. Furthermore, the ethylene twisting process is studied.

Relativistic coupled cluster (RCC) computation of the electric dipole moment enhancement factor of francium due to the violation of time reversal symmetry.

A relativistic many-body theory for the electric dipole moment (EDM) of paramagnetic atoms arising from the electric dipole moment of the electron is presented and implemented. The relativistic coupled-cluster method with single and double excitations (RCCSD) using the Dirac-Coulomb Hamiltonian and a weak parity and time reversal violating interaction to the first-order of perturbation has been employed to obtain the EDM enhancement factor for the ground state of the Fr atom due to the intrinsic EDM of the electron. The trends of different correlation effects and the leading contributions from different physical states are discussed.

An explicitly spin-free compact open-shell coupled cluster theory using a multireference combinatoric exponential ansatz: formal development and pilot applications.

In this paper, we present a comprehensive account of an explicitly spin-free compact state-universal multireference coupled cluster (CC) formalism for computing the state energies of simple open-shell systems, e.g., doublets and biradicals, where the target open-shell states can be described by a few configuration state functions spanning a model space.

A companion perturbation theory for state-specific multireference coupled cluster methods.

A partitioning scheme is applied to the state-specific Mukherjee multireference coupled cluster method to derive a companion perturbation theory (Mk-MRPT2). A production-level implementation of Mk-MRPT2 is reported. The effectiveness of the Mk-MRPT2 method is demonstrated by application to the classic F(2) dissociation problem and the lowest-lying electronic states of meta-benzyne, including computations with up to 766 atomic orbitals.