C. R. Sarma's research while affiliated with Indian Institute of Technology Bombay and other places

Publications (60)

Article
Fermion operator realization of the Lie-algebra of SCX(N) (N = 2n, 2n + 1) has been used extensively to study the symmetry adaptation of the fundamental spinor space of SO(N) to SO(3). However, the multispinor basis cannot be handled directly using such fermion operators since they generate only the totally antisymmetric irreducible representation...
Article
The determination of the subduction coefficients for states of the unitary group U(n) under the restrictions U(n) ↓ U(n1) ⊗ U(n2) have been considered for the spin free states of many electron systems. Using the transformation properties of the tensor basis spanning the irreducible representation 〈2N/2–S, 12S〉 of U(n) under the permutations of elec...
Article
A spin-free polynomial representation of antisymmetrized geminal products is presented for several cases. In particular, products of identical geminals, which possess different spin multiplicity, are considered. The cases of singlet geminals, singlet geminals with one or two triplet geminals coupled to the lowest possible spin multiplet, and triple...
Article
Full-text available
The present approach is a graphical technique for representing and generating primitive configurations of space orbitals for electronic systems. The graph is developed as a tree whose paths define the allowed space configurations of electrons admitting at most double occupancy for each orbital. The emphasis in the graph is on the nodes representing...
Article
A graphical technique is proposed for generating and addressing all required α and β strings of spin-orbitals for configuration interaction treatments based on determinants. Compared with other treatments, this scheme, as well as reducing to a minimum the number of logical operations, avoids entirely the storage of the massive tables and vectors us...
Article
A structure-dependent labeling scheme for the Standard Young Tableaux spanning the representations of the permutation group is outlined in the present work. This scheme is used to generate the representations of a select class of permutations such as dense cycles and general transpositions of the group using minimal storage requirements. Two distin...
Article
We present a graphical technique for generating and indexing spin monomials of high-spin systems. The procedure consists of developing a graph with at most n line segments from each node in a given row to the one immediately lower, where n is the multiplicity of single-particle spin function. The paths lead to monomials with definite M values at ea...
Article
In the present article, we outline a simple scheme for generating configuration interaction matrix elements for spin)orbit interactions in molecules. The procedure leads to a close parallelism with spin-free permutation-group approaches. Unitary shift operators were successfully used on the orbital space to generate the matching permutations necess...
Article
A reduction of the inner product space of the permutation group on an N-particle system has been used to develop a scheme for obtaining the states spanning a general irreducible representation of the unitary group U(nm) in terms of those spanning the product representations of U(n)(X)U(m). Since relatively straightforward methods are now available...
Article
A non-genealogical method is proposed for the reduction of the inner product representations of the permutation group SN. This method of determining the Clebsch-Gordan coefficients has been found to be recursive only within a given series. As such it permits the direct reduction of products of large-dimensional representations.
Article
A simple procedure is outlined for adapting the basis spanning the irreducible representations of the permutation group S(N) to those spanning the product representations of the subgroup S(N1)*S(N2) where N1+N2=N. An algorithm based on the procedure is also discussed.
Article
A Monte Carlo sampling technique based on 2*2 rotations of the Heisenberg spin-1 Hamiltonian containing both anisotropic and next-nearest-neighbour (NNN) terms has been attempted. Closed rings of six, eight, 10 and 12 spin-1 sites have been studied and the ground and the first excited states have been obtained. The validity of the procedure has als...
Article
The problem of three spin deviations from a fully aligned state is studied for the Heisenberg model with next-nearest-neighbour interactions for the case of spin 1. The method used is a straightforward generalization of the equation-of-motion method of Fukuda and Wortis, taking care of the unphysical states. The resulting integral equation is solve...
Article
A procedure has been outlined for generating configuration space basis states of many-particle systems in which the maximal occupancy of any single-particle orbital is arbitrary. An efficient computer program has been developed for determining the matrix elements of the generators of the unitary group U(n) over configuration space basis states. Com...
Article
A procedure for obtaining an angular momentum projected space-spin basis for multishell configurations (j1N1 j2N2...jkNk) of nucleons in a specified isospin state (N, T) is outlined. The scheme is based on generating the tensor basis spanning such an irreducible representation of the unitary group adapted to the non-canonical subgroup U(n1)(X)...(X...
Article
A procedure has been outlined for obtaining the scalar factors (reduced Wigner coefficients) of the unitary group U(nm) contains/implies U(n)(X)U(m). This has been done at the permutation group level for SN down arrow SN'(X)SN" and the equality between the scalar factors of these two groups has been exploited. It has been shown that the scalar fact...
Article
The classes of the symmetric group script J signN are identified by partitions of N. In this work an indexing scheme is presented which provides a dense enumeration of the classes of script J signN. The method is based on a graphical representation of partitions of N, which also enables the determination of the class corresponding to a given number...
Article
The classes of the symmetric group N are identified by partitions of N. In this work an indexing scheme is presented which provides a dense enumeration of the classes of N. The method is based on a graphical representation of partitions of N, which also enables the determination of the class corresponding to a given number. © 1997 John Wiley & Sons...
Article
A technique for the configuration interaction (CI) study of many-electron systems is developed based on Rumer spin-coupling scheme for the antisymmetrized configuration state functions (CSF). Incorporating a new graphical approach, the primitive configurations have been generated in blocks of definite ionocities to permit ready association of possi...
Article
A simple procedure is presented for obtaining the standard Young tableaux for the representation [(N/2) + S,(N/2) − S] of the permutation group ℒN for an N-electron system in spin state S directly from the spin branching diagram. We redefine the coordinate axes of the branching diagram to obtain a graph in terms of the partitions of the two-rowed Y...
Article
In the present article, we have attempted a systematic procedure for use of biorthogonal techniques to the configuration interaction studies in molecules using nonorthogonal valence bond (VB) orbitals. The procedure developed is integral-driven and a program based on this has been developed. Test runs of the program have been carried out in case of...
Article
In the present note we outline a truncation scheme for configuration space ofN-electron systems in definite spin statesS for Hubbard Hamiltonian with first neighbour transfer terms. For this sparse matrix we find that the present truncation scheme yields reasonably good ground and first excited states with very limited space being used.
Article
In the present note, a linked form of spin-paired functions for an N-electron system in spin state S is suggested. This is found to lead to a simple scheme for generating the representation matrices of the elements of permutation group without searching for linkages in the superposition diagrams. The program based on this is found to generate the r...
Article
A direct graphical approach is presented for the evaluation of matrix elements of a spin-free Hamiltonian between Slater determinants of nonorthogonal orbitals. The matrix element contributions are obtained by repeated use of N – 2 electron minors of the overlap matrix that are generated by independent looping of reduced N – 2 electron graphs for t...
Article
An indexing scheme for determinantel states of spin-orbitals that enables a dense contiguous labeling of configurations even for truncated limited configuration-interaction expansions of the many-electron wavefunction is presented.
Article
An exploitation of the Rumer-Weyl basis of the valence bond (VB) formalism within the Clifford algebra unitary group approach (CAUGA) scheme is formulated. Simple rules are given for the construction of the relevant non-orthogonal bi-spinor Clifford-Weyl basis, whose vectors can be conveniently labeled with UGA step numbers, as well as simple rules...
Article
An alternative formalism leading to a vectorizable algorithm for a large scale full or limited configuration interaction (CI) calculations, employing partially spin-adapted bi-spinor or Hartree-Waller-type determinantal basis, is outlined and its relationship to existing approaches and algorithms is briefly discussed.
Chapter
Spinor representations of generators of the Lie algebra of SO(N)(N=2n, 2n+1; n integer, have played a key role in a number of areas of Physics [1–5]. A general approach to these representations in a form suitable for practical applications has been of recent origin [6–8]. Starting with the unitary algebra of U(2n), the generators of SO(N) and U(n)...
Article
A simple procedure has been created for indexing the spin-free configurations of an N-electron system in spin state S. This indexing has been linked to a procedure for generating the matrix representations of the generators of the unitary group U(n) to enable a direct configuration study to be undertaken.
Article
The unitary group approach has been used to study the pair correlated ground states of identical nucleon systems. Both odd- and even-nucleon systems have been studied. The Pauli principle and number conservation have been shown to follow in a natural manner in this formalism. A simple algorithm has been developed based on the method and applied to...
Article
Pair correlated angular momentum projected standard Weyl tableau states spanning an m-dimensional paired shell-model space have been obtained for a system of 2N identical nucleons. A simple procedure has been developed for carrying out the restriction of the unitary group U(m) to the rotation group O(3) for configurations of both single and multile...
Article
Unitary group approach (UGA) to the many‐electron correlation problem is generalized by embedding the unitary group U(n) in a much larger group U(2n) via the rotation groups SO(m) with m=2n or 2n+1 and their covering group Spin (m). Exploiting the spinorial Clifford algebra basis associated with Spin (m), it is shown that an arbitrary N‐electron co...
Article
The boson basis for the fermion shell-model problem has been realized over a representation space Vn(n−1)/2 of the unitary group U(n(n−1)/2). A contraction of this space was found to yield the generator algebra of U(n). Based on this result it is shown that the transformations induced by the Dyson-mapped boson Hamiltonian on the Dyson boson basis a...
Article
A realization of the spinor algebra of the rotation group SO(N), N=2n or 2n+1, in the covering algebra of U(2n) is exploited to obtain explicit representation matrices for the SO(N) generators in the basis adapted to the subgroup chain SO(N)⊃U(n)&supuline;U(n−1)⊃⋅⋅⋅⊃U(1). As a special case the computation of matrices of U(n) representations charact...
Article
The generators of the rotation groups SO(N) (N=2n, 2n+1) have been realized using a restriction of the unitary group U(2n) defined on the 2n ‐dimensional fundamental representation space of spinors. These generators have been used to subduce multispinor representations of SO(N) from those of U(2n). The procedure has been illustrated for the two‐spi...
Article
Double Gel’fand polynomials of boson operators spanning the irreducible representation [m] of U(n) in U(n)*U(n) have been obtained using symmetrized linear combinations of Wigner operators of the permutation group. The normalized coefficients which occur in the polynomial representation have been expressed as linear combinations of the Young or...
Article
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Article
A direct method for the reduction of inner products of irreducible representations (irreps) of unitary groups has been proposed using the duality between the permutation and unitary groups. A canonical tensor basis set has been used to obtain a closed expression for the Clebsch–Gordan coefficients of U(n). This expression involves the subduction co...
Article
Symmetry adaptation of spin–free multishell electron configurations in molecules to general non-Abelian point groups has been carried out. Using the basis spanning the irreducible representation [2N/2−S, 12S, 0n−N/2−S] of the unitary group U(n) as primitives, the Wigner operators for point groups were applied to generate the required basis. In the...
Article
A direct procedure is outlined for determining the basis spanning finite dimensional irreducible representations of U( p+q) adapted to the subgroup U( p)⊗U( q). Using a tableau based analysis, it is shown that the realization of the semimaximal states follows readily from a knowledge of the matrix elements of the generators Ei+1 of U( p), U( q)⊆U(...
Article
This chapter studies many-electron systems using tensor bases for the irreps of the unitary group. Various ways of enumerating the basis states of the unitary group have been discussed. Procedures for calculation of configuration interaction (CI) matrix elements have been described. The discussion of the basis states of irreps of U (n) is general e...
Chapter
Many-particle states defining a basis spanning an irreducible representation of the Unitary Group U(n) have been obtained by reduction of the space of orbital tensor products. This approach has been found to lead to a simple diagrammatic technique for evaluation of matrix elements of generators of U(n). Applications to electronic configurations in...
Article
A simplification has been attempted in the procedures for determining the matrix elements of the generators of the unitary group U(n) over a tensor basis spanning the irreducible representation 2 N/2–S , 1 2S for an N-electron system. It has been shown that these matrix elements require, for their determination, only the corresponding representatio...
Article
The symmetry of the Nth rank tensor basis for an irreducible representation of U (n) under the operations of the permutation group has been investigated. It has been found that symmetrized linear combinations of the elements of the matrix algebra of SN lead to a tensor basis for U (n) yielding the same matrix elements as the Gel'fand-Tsetlin basis...
Article
A procedure is described for generating the many-particle states belonging to an irreducible representation of the unitary group. A representation of this basis has been introduced which is appropriate in limited configuration interaction studies. On leave from Indian Institute of Technology, Bombay, India.
Article
A procedure is outlined for a programmable spin-free configuration-interaction (CI) study in molecules using single-parameter alternant molecular orbitals for generating various configurations. The configurations were chosen to form bases for the irreducible representation {2N/2–2, 12S} of the general linear group GL(n). Using a transformation to b...
Article
The transformation properties of a projected basis for the irreducible representation (IR), {2N/2−S,12S}, of U(n) under the elementary generators of the group have been studied. It has been found that these transformations are identical (to within a phase factor) with those of the standard bases spanning the given IR. The correspondence between thi...
Article
Based on the formalism developed in a recent note, we have worked out a program for CI calculations in molecules. In the present note, the details of the program are discussed. The usefulness of the program has been illustrated using some calculations.
Article
In this note a method is presented for quick implementation of configuration interaction (CI) calculations in molecules. A spin-free Hamiltonian for anN electron system in a spin stateS, expressed in terms of the generators for the unitary group algebra, is diagonalized over orbital configurations forming a basis for the irreducible representation...
Article
The transformation properties of a projected basis for the irreducible representation (IR), {2N/2-S,12S}, of U(n) under the elementary generators of the group have been studied. It has been found that these transformations are identical (to within a phase factor) with those of the standard bases spanning the given IR. The correspondence between thi...
Article
A new method is presented for obtaining the spin eigenfunctions of 2n electron systems in the spin state S and MS = 0. Using a modified Young operator the function for the state S, MS ( = S) of the system is first projected out. The projected function is then symmetrized over the last n particles and the weight lowering operator Š is then applied t...
Article
A method for the construction of the essentially idempotent and Hermitian diagonal elements of the matric algebra of the permutation group Sn is proposed. For the irreducible representation [λ] = [λ1, λ2] characterising a spin state S of an n-electron system, it is found that this method generates the complete set of spin projections from the appro...
Article
An operator method is presented for realising coupled spin functions for n-electron systems in a pure spin state. The operator is realised in an essentially idempotent form as a combination of a conventional spin projector and a matric projector on the spin system.
Article
An empirical scheme of parametrization of the CNDO is presented which satisfies the invariance requirements of the method. Calculation of single bond and orbital energies are presented for a number of symmetric triatomic molecules.
Article
A semiempirical calculation of single bond energies and dipole moments of diatomic molecules is presented using an empirical form for the two electron repulsion integral. Assuming, in addition, a form for the resonance integral, the bond stretching force constants are also evaluated.
Article
The determination of the subduction coefficients for states of the unitary group U(n) under restrictions U(n) down arrow U(nâ) x U(nâ has been considered for the spin-free states of many electron systems. With the aid of the transformation properties of the tensor basis spanning the irreducible representation of U(n) under the permutations of elec...

Citations

... A step forward in this direction was the development of the Clifford algebra UGA (CAUGA) [32,81,98,114,115] that is based on the work of Sarma and collaborators [116,117]. Here, in lieu of G-T chain one exploits the imbedding of U(n) in a much larger group U(2 n ) via the special orthogonal group SO(m), m = 2n or m = 2n + 1 (i.e., the classical LAs B n and D n ) and their covering group Spin(m), i.e., the group chain ...
... In their works simplifications on the computation techniques were outlined. Other similar works can be found in Refs [7]- [10]. Kent and Schlesinger proposed the distinct row tabular graphical (DRTG) method for the UGA, [11−13] which enables them to derive explicit expressions for a part of matrix elements of two-body operators. ...
... A year later, Olsen and co-workers succeeded in passing the billion determinant limit, 2 and the combined achievements of these two groups [3][4][5][6] were long regarded by many in the community as heralding a new age of exact electronic structure theory, spawning a number of additional developments in the area over the following years. [7][8][9][10][11][12][13] Since the 1990s, however, much of the optimism surrounding standard FCI theory has faded. While boundaries continue to be pushed today, 14,15 it has now become abundantly clear that truly exact theory will never successfully evolve into a widely applicable commodity tool, at least not by means of classical computing, [16][17][18][19][20][21][22] and the emergence of its quantum counterpart is not guaranteed to offer a practical panacea either. ...
... 598 A spin-unpolarized singlet and a spin-polarized triplet state at DFT level of theory were fitted with 3768 data points. 598,599 This two-state spin-diabatic problem allowed for evaluation of coupling values and singlet-triplet transitions with the fewest switches surface hopping approach. 403,404 In a later study, another adiabatic spin-polarized PES was included and coupling values were computed between singlets and triplets 600 and evaluated from constructed Hamiltonian matrices. ...
... As a starting point for the induction, we now consider the case of r = j = 1 and find in analogy to Eq. (23) that (42) ...
... In present large-scale configuration interaction algorithms, the Slater determinants are usually addressed by a double index (I α , I β ) formed by a separate index I α for the α-string of N α spin orbitals associated with α spin and an index I β for the β-string for the remaining N β electrons [13][14][15][16][17][18]. To improve the addressing of determinants in large-scale CI computations, Sarma et al. [19] recently successfully presented a dense vertex-based indexing scheme that minimized the number of logical and search operations. By this scheme, which had previously been applied in connection with permutation group algebras [20,21], it was possible to avoid the use of intermediate addressing tables. ...
... Over the past 3 decades its applications in mathematical/theoretical chemistry has reaped numerous advances: starting in the 1980s, Geometric Algebras were used as part of a unitary group approach to generate quantum chemical, finite-dimension, orbital models of many-electron systems [1,2]. Additionally, Geometric Algebra was used to realise and exploit the Rumer-Weyl basis of valence bonds [3,4]. Geometric Algebra was also utilised as a potential tool to assist molecular modellers in solving a range of conformational problems [5]. ...
... In closing this series, let us at least mention some other-more "exotic"-developments related to UGA and to fermionic algebras in general (for a brief overview see Ref. [39]). In particular, we should note the fundamental role played here by Clifford algebras and by the related group U(2 n ) while exploiting the group chain [34,[40][41][42][43][44][45][46] where m = 2n + 1 or m = 2n . These ideas led to a development of the so-called Clifford algebra UGA (CAUGA) [34,[40][41][42][43][44][45][46], which proved to be useful in applications that are based on the coupled cluster (CC) approaches or in those exploiting the valence bond (VB) formalism, using the semi-empirical Pariser-Parr-Pople (PPP) Hamiltonian in the PPP-VB scheme [47][48][49]. ...
... Based on the FORSSCF and CASSCF methods, let the sum of electrons be N, the sum of orbitals be n in orbital variance space of the molecule, the number of core orbitals be no, the number of core electrons be No, the number of active orbitals be na, the number of active electrons be Na, and the number of virtual orbitals be nv, then N = No + Na, (1) n = no + na + nv. (2) Suppose that the one-electron orbitals consist of SLMOs: re(l, 1), m(2, 1) .... , m(j, i), ..., m(n, d), where the first are core orbitals, those in the middle are active orbitals, and the latter are virtual orbitals, re(j, i) expresses SLMO, j is an orbital notation, i is the notation of subspace spanned by equivalent orbitals, and d is the sum of subspaces. Let g be the group element of molecular point group G, then all re(j, i) satisfy ...
... Solutions to Hamiltonian which are also eigenfunctions ofŜ 2 with eigenvalue S(S + 1) will have 2S + 1 degeneracy corresponding to the eigenvalues ofŜ z when no magnetic field is present. As the solution tô H el is computationally costly 13 , working in spin eigenbasis is a way to reduce the computation cost by working in subspace, which has been extensively used by physicists and chemists in standard computation [14][15][16] . Similarly, working in spin eigenbasis provides speed up for simulating electronic structure on quantum computers 11,17 . ...