341 research outputs found
Replication Data for: Bird’s Decision to Shift the Direction of Migration Path Depends on the Position of Sun as well as Moon: A Directional Statistical Inference
No full textDataset for: Bird’s Decision to Shift the Direction of Migration
Path Depends on the Position of the Sun as well as Moon:
A Directional Statistical Inference
(Author: Prithwish Ghosh, Debashis Chatterjee, Amlan Banerjee
A universal explicit electron correlation correction applied to Mukherjee's multi-reference perturbation theory
No full textWe present a universally applicable explicit electron correlation (F12) correction and apply it to Mukherjee's multi-reference perturbation theory (Mk-MRPT2). Two different F12 corrections are proposed: one is a universal F12 correction which is added to the conventional orbital correction, which is referred to as Mk-MRPT2+F12. In the second type of F12 correction the individual F12 contributions are added to each matrix element of the effective Hamiltonian. Subsequent diagonalization yields the Mk-MRPT2-F12 correction. Thereby, we achieve for both F12 corrections the accuracy of a quadruple-zeta basis set calculation when a triple-zeta basis set is employed and the F12 correction is added. Both F12 corrections reduce to MP2-F12/1A (fixed) in the single-reference limit. (C) 2012 Elsevier B.V. All rights reserved.Chemistry, PhysicalPhysics, Atomic, Molecular & ChemicalSCI(E)EI0ARTICLE247-25153
The Structural Relationship between Current and Capital Account Balance in India: A Time Series Analysis
No full textThe long run relationship between current account balance (CAB) and capital account balance (KAB) and the repercussions of capital account convertibility (KAC) on growth process of a country is a much debated issue. In particular, in the aftermath of the Southeast Asian crisis, the limitation of the liberal capital regime for a developing country like India is often highlighted in the literature. However, the probable impact of introducing KAC on CAB in India generally is discussed theoretically. Though some of the existing studies in India have earlier focused on this research question, they have done so by exogenously assuming the existence of a single structural break in the interrelationship between CAB and KAB. The present study intends to bridge the gap in the literature by raising two empirical questions: first, how far KAC is likely to destabilize the CAB and second, measuring the strength of the interrelationship between CAB and KAB. The current paper also contributes to the literature by incorporating multiple endogenous structural breaks in the empirical analysis. The empirical findings do not support any long term relationship between capital and current account balance and reveals that two significant structural breaks are observed in 1993-94 and 2003-04.International Capital Movements, Foreign Exchange, Current Account Adjustment
Irreducible Brillouin conditions and contracted Schrodinger equations for n-electron systems. II. Spin-free formulation
No full textRecently [W. Kutzelnigg and D. Mukherjee, Chem. Phys. Lett. 317, 567 (2000); D. Mukherjee and W. Kutzelnigg, J. Chem. Phys 114, 2047 (2001)] the irreducible k-particle Brillouin conditions IBCk and the irreducible k-particle contracted Schrodinger equations ICSEk were derived. These permit the definition of a hierarchy of k-particle approximations for the direct calculation of the cumulants λk of the k-particle density matrices. Now, the spin-free form of these conditions, appropriate for a spin-free Hamiltonian, is given. This is particularly useful for open-shell states. The definition of the cumulants of the reduced densities has to be generalized for these anyway, making use of irreducible tensor operators with respect to SU2. There are two alternative definitions of spin-free cumulants, of which the one in terms of spin-free reduced density matrices appears to be preferable. Alternatively to the straight spin-free formulation, we also present a theory in terms of spin-free operators adapted to the symmetric group. Partial trace relations that relate the elements of the cumulants of different particle rank are derived. There are partial trace relations for "exchange elements," which are determined by the total spin quantum number S. From these relations the individual exchange elements of Λ2 can be obtained in special cases. This allows a simple formulation of the stationarity conditions for open-shell states of any spin multiplicity
On the hierarchy equations of the wave-operator for open-shell systems
No full textStarting with the open-shell analogue of the Gell Mann-Low theorem of many-body perturbation theory, a non-perturbative linear operator equation is derived for the linked part of the wave-operator W for open-shell systems. It is shown that, for a proper treatment of the linked nature of the wave-operator, a separation into its connected and disconnected components has to be made, and this leads to a hierarchy of equations for the various connected components. It is proved that the set of equations can be cast into a form equivalent to the non-perturbative equations of the wave-operator recently derived by Mukherjee and others in a coupled-cluster or exp (T) type formalism if a consistent use is made of a 'core-valence separability' condition introduced earlier. A comparison of the coupled-cluster representation of W with the perturbative representation reveals that various alternative forms of W in the coupled-cluster representation are possible and these reflect alternative ways of realising the core-valence expansion of the wave-operator. In particular it is emphasised how the use of Mandelstam block-ordering simplifies the coupled-cluster theories to a considerable extent and a comparison is made with coupled-cluster methods for open-shells put forward very recently by Ey and Lindgren. Finally, it is shown how difference energies of interest may be derived in a compact manner using the Mandelstam block-ordering of the wave-operator
A spin-adapted size-extensive state-specific multi-reference perturbation schemes. I. Formal developments
No full textWe 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-Schrodinger (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. (C) 2012 American Institute of Physics. [doi:10.1063/1.3672083]Physics, Atomic, Molecular & ChemicalSCI(E)EI16ARTICLE2null13
Multireference perturbation theory: the n-electron valence state perturbation theory approach
No full textA few general considerations concerning Multireference Perturbation Theory (MRPT) approaches are firstly reported, focusing in particular on the concepts of contraction (internal and external), of quasi-degeneracy (actual and artificial), and of first order interacting space. As a particular case of MRPT method,
the n-electron Valence State Perturbation Theory (NEVPT) is described in some details clarifying its main properties and focusing on the interpretation of the energies appearing in the perturbation denominators in terms of physical processes taking place in the active space. Finally, the problems arising in MRPT in presence of a correlation-induced relaxation of the molecular orbitals (also called Brueckner effect in the Coupled Cluster field) are shortly discussed, using the singlet pi -> pi* excited state of the ethylene molecule as an example
Use of a convenient size-extensive normalization in multi-reference coupled cluster (MRCC) theory with incomplete model space: a novel valence universal MRCC formulation
No full textWe present in this paper a size-extensive formulation of a valence universal multi-reference coupled cluster (VU-MRCC) theory which uses a general incomplete model space (IMS). The earlier formulations by Mukherjee [D. Mukherjee, Chem. Phys. Lett. 125 (1986) 207] led to size-extensive Heff which was both connected and 'closed', thereby leading to size-extensive energies. However, this necessitated abandoning the intermediate normalization (IN) for the valence universal wave-operator Ω when represented as a normal ordered exponential cluster Ansatz Ω={exp(S)} with S as the cluster operator. The lack of IN stemmed from the excitation operator Sq-op which leads to excitations into the complementary model space by their action on at least one model function. The powers of Sq-op can in general bring a model function Φi back to another model function Φj, and this is the reason why Ω does not respect IN. Sq-op are all labelled by active orbitals only. To achieve connectivity of Heff, it must be a 'closed' operator. A closed operator is one which always produces a model function by its action on another model function. Since the decoupling conditions Lq-op=0, and Lop=0 for the transformed operator L=Ω-1HΩ would be in conflict with Ωq-op=1q-op, the model space projection of Ω, PΩP=P cannot be maintained for the normal ordered Ansatz. This leads to a somewhat awkward expression for Heff. Bera et al. [N. Bera, S. Ghosh, D. Mukherjee, S. Chattopadhyay, J. Phys. Chem. A 109 (2005) 11462] recently tried to simplify the expression for Heff, and accomplished this by introducing suitable counter-terms Xcl in Ω to enforce Ωcl=1cl. We show in this paper that Heff in this formulation leads to a disconnected Heff, though it is equivalent by a similarity transformation to a connected effective hamiltonian H¯eff. Guided by the insight gleaned from this demonstration, we have proposed in this paper a new form of the wave-operator which never generates any powers of Sq-op, which is closed. This 'externally projected' wave-operator does not need counter-terms Xcl and automatically ensures Ωcl=1cl, thereby yielding directly a closed connected H¯eff. The desirable features of the traditional normal ordered Ansatz, such as the valence universality, subsystem embedding conditions hierarchical decoupling of the VU-MRCC equations for decreasing valence ranks are all satisfied by this new Ansatz for the wave-operator
Is there any relationship between Economic Growth and Human Development? Evidence from Indian States
No full textThe paper attempts to analyse the relationship between economic growth and human development for 28 major Indian States during four time periods ranging over last two decades: 1983, 1993, 1999-00 and 2004-05. To construct Human Development Index for Indian States, we consider the National Human Development Report 2001 Methodology. The objective of this exercise to understand at what degree and extent the per capita income (as an indicator of economic growth) has influenced the human development across Indian States. To understand the rural – urban disparity in the achievement of human development, the Human Development Index is constructed for rural and urban areas separately for each of the States. The result shows that that per capita income is not translating into human well being. This perhaps in another way might signify the rising influence of other variables in determination of the HD achievements of a state. The result shows the need for further investigation to determine the underlying factors (other than per capita income) which influence HD achievements of a State.Economic Growth; Human Development; Human Development Index Methodology; Economic Liberalisation; Indian States
An algebraic proof of generalized Wick theorem
No full textThe multireference normal order theory, introduced by Kutzelnigg and Mukherjee [J. Chem. Phys. 107, 432 (1997)] , is defined explicitly, and an algebraic proof is given for the corresponding contraction rules for a product of any two normal ordered operators. The proof does not require that the contractions be cumulants, so it is less restricted. In addition, it follows from the proof that the normal order theory and corresponding contraction rules hold equally well if the contractions are only defined up to a certain level. These relaxations enable us to extend the original normal order theory. As a particular example, a quasi-normal-order theory is developed, in which only one-body contractions are present. These contractions are based on the one-particle reduced density matrix
- …
