Publications (17)40.52 Total impact
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ABSTRACT: An analytic scheme is presented for the evaluation of first derivatives of the energy for a unitary group based spinadapted coupled cluster (CC) theory, namely, the combinatoric openshell CC (COSCC) approach within the singles and doubles approximation. The widely used Lagrange multiplier approach is employed for the derivation of an analytical expression for the first derivative of the energy, which in combination with the wellestablished densitymatrix formulation, is used for the computation of firstorder electrical properties. Derivations of the spinadapted lambda equations for determining the Lagrange multipliers and the expressions for the spinfree effective density matrices for the COSCC approach are presented. Orbitalrelaxation effects due to the electricfield perturbation are treated via the Zvector technique. We present calculations of the dipole moments for a number of doublet radicals in their ground states using restricted openshell HartreeFock (ROHF) and quasirestricted HF (QRHF) orbitals in order to demonstrate the applicability of our analytic scheme for computing energy derivatives. We also report calculations of the chlorine electricfield gradients and nuclear quadrupolecoupling constants for the CCl, CH2Cl, ClO2, and SiCl radicals.The Journal of chemical physics. 09/2014; 141(10):104102.  [Show abstract] [Hide abstract]
ABSTRACT: The novel multireference equationofmotion coupledcluster (MREOMCC) approaches provide versatile and accurate access to a large number of electronic states. The methods proceed by a sequence of manybody similarity transformations and a subsequent diagonalization of the transformed Hamiltonian over a compact subspace. The transformed Hamiltonian is a connected entity and preserves spin and spatial symmetry properties of the original Hamiltonian, but is no longer Hermitean. The final diagonalization spaces are defined in terms of a complete active space (CAS) and limited excitations (1h, 1p, 2h, …) out of the CAS. The methods are invariant to rotations of orbitals within their respective subspaces (inactive, active, external). Applications to first row transition metal atoms (Cr, Mn, and Fe) are presented yielding results for up to 524 electronic states (for Cr) with an rms error compared to experiment of about 0.05 eV. The accuracy of the MREOM family of methods is closely related to its favorable extensivity properties as illustrated by calculations on the O2O2 dimer. The computational costs of the transformation steps in MREOM are comparable to those of closedshell Coupled Cluster Singles and Doubles (CCSD) approach.The Journal of Chemical Physics 02/2014; 140(8):081102. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We present a symbolic manipulation algorithm for the efficient automated implementation of rigorously spinfree coupled cluster (CC) theories based on a unitary group parametrization. Due to the lack of antisymmetry of the unitary group generators under index permutations, all quantities involved in the equations are expressed in terms of nonantisymmetric tensors. Given two tensors, all possible contractions are first generated by applying Wick’s theorem. Each term is then put down in the form of a nonantisymmetric Goldstone diagram by assigning its contraction topology. The subsequent simplification of the equations by summing up equivalent terms and their factorization by identifying common intermediates is performed via comparison of these contraction topologies. The definition of the contraction topology is completely general for nonantisymmetric Goldstone diagrams, which enables our algorithm to deal with noncommuting excitations in the cluster operator that arises in the unitary group based CC formulation for openshell systems. The resulting equations are implemented in a new code, in which tensor contractions are performed by successive application of matrix–matrix multiplications. Implementation of the unitary group adapted CC equations for closedshell systems and for the simplest openshell case, i.e., doublets, is discussed, and representative calculations are presented in order to assess the efficiency of the generated codes.Journal of Chemical Theory and Computation 05/2013; · 5.39 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Extensions of multireference equation of motion coupled cluster theory (MREOMCC) [D. Datta and M. Nooijen, J. Chem. Phys. 137, 204107 (2012)] are presented that include additional correlation effects into the global, internally contracted similarity transformation, induced by the cluster operators. As a result the final uncontracted diagonalization space can be more compact than in the parent MREOMCC approach. A wide range of applications, including transition metal atomic excitation spectra, a large set of valence excited states of organic compounds, and potential energy surfaces of ground and excited states of butadiene, is presented to benchmark the applicability of the parent MREOMCC methodology and its new variations.The Journal of Chemical Physics 04/2013; 138(13):134108. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A generalization of the equationofmotion coupled cluster theory is proposed, which is built upon a multireference parent state. This method is suitable for a number of electronic states of a system that can be described by similar active spaces, i.e., different linear combinations of the same set of active space determinants. One of the suitable states is chosen as the parent state and the dominant dynamical correlation is optimized for this state using an internally contracted multireference coupled cluster ansatz. The remaining correlation and orbital relaxation effects are obtained via an uncontracted diagonalization of the transformed Hamiltonian, Ĥ=e(T̂)Ĥe(T̂), in a compact multireference configuration interaction space, which involves configurations with at most single virtual orbital substitution. The latter effects are thus statespecific and this allows us to obtain multiple electronic states in the spirit of the equationofmotion coupled cluster approach. A crucial aspect of this formulation is the use of the amplitudes of the generalized normalordered transformed Hamiltonian Ĥ as the residual equations for determining the internally contracted cluster amplitudes without any projection onto the excited configurations. These residuals have been termed as the manybody residuals. These equations are formally nonsingular and thus allow us to solve for all amplitudes without discarding any, in contrast to other internally contracted approaches. This is desirable to ensure transferability of dynamical correlation from the parent state to the target states. Preliminary results involving the lowlying electronic states of C(2), O(2), and the excitation spectra of three transition metal atoms, e.g., Fe, Cr, and Mn, including hundreds of excited states, illustrate the potential of our approach.The Journal of Chemical Physics 11/2012; 137(20):204107. · 3.12 Impact Factor  The Journal of Chemical Physics 08/2012; 137(6):069901. · 3.12 Impact Factor
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ABSTRACT: One generic difficulty of most statespecific manybody formalisms using the JeziorskiMonkhorst ansatz: ψ = Σ(μ)exp(T(μ))φ(μ)>c(μ) for the waveoperators 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 excitationsthough linearly independentare far too numerous. It is well known from the success of the contracted multireference configuration interaction (MRCI(SD)) that, at least for the inactive double excitations, their model space dependence (μdependence) is weak. Considerable simplifications can thus be obtained by using a partially internally contracted description, which uses the physically appealing approximation of taking the inactive excitations T(i) to be independent of the model space labels (μindependent). We propose and implement in this paper such a formalism with internal contractions for inactive excitations (ICI) within Mukherjee's statespecific multireference coupled cluster theory (SSMRCC) framework (referred to from now on as the ICISSMRCC). To the extent the μindependence of T(i) is valid, we expect the ICISSMRCC to retain the conceptual advantages of sizeextensivity yet using a drastically reduced number of cluster amplitudes without sacrificing accuracy. Moreover, greater coupling is achieved between the virtual functions reached by inactive excitations as a result of the internal contraction while retaining the original coupling term for the μdependent excitations akin to the parent theory. Another major advantage of the ICISSMRCC, unlike the other analogous internally contracted theories, such as ICMRCISD, CASPT2, or MRMP2, is that it can use relaxed coefficients for the model functions. However, at the same time it employs projection manifolds for the virtuals obtained from inactive n holen particle (nhnp) excitations on the entire reference function containing relaxed model space coefficients. The performance of the method has been assessed by applying it to compute the potential energy surfaces of the prototypical H(4); to the torsional potential energy barrier for the cistrans isomerism in C(2)H(4) as well as that of N(2)H(2), automerization of cyclobutadiene, single point energy calculation of CH(2), SiH(2), and comparing them against the SSMRCC results, benchmark full CI results, wherever available and those from the allied MR formalisms. Our findings are very much reminiscent of the experience gained from the ICMRCISD method.The Journal of Chemical Physics 04/2012; 136(16):164104. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A statespecific partially internally contracted multireference coupled cluster approach is presented for general complete active spaces with arbitrary number of active electrons. The dominant dynamical correlation is included via an exponential parametrization of internally contracted cluster operators ( ̂T) which excite electrons from a multideterminantal reference function. The remaining dynamical correlation and relaxation effects are included via a diagonalization of the transformed Hamiltonian ̅Ĥ =e( ̂T)Ĥe( ̂T) in the multireference configuration interaction singles space in an uncontracted fashion. A new set of residual equations for determining the internally contracted cluster amplitudes is proposed. The second quantized matrix elements of ̅Ĥ , expressed using the extended normal ordering of Kutzelnigg and Mukherjee, are used as the residual equations without projection onto the excited configurations. These residual equations, referred to as the manybody residuals, do not have any nearsingularity and thus, should allow one to solve all the amplitudes without discarding any. There are some relatively minor remaining convergence issues that may arise from an attempt to solve all the amplitudes and an initial analysis is provided in this paper. Applications to the bondstretching potential energy surfaces for N(2), CO, and the lowlying electronic states of C(2) indicate clear improvements of the results using the manybody residuals over the conventional projected residual equations.The Journal of Chemical Physics 06/2011; 134(21):214116. · 3.12 Impact Factor 
Article: The spinfree analogue of Mukherjee's statespecific multireference coupled cluster theory.
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ABSTRACT: In this paper, we develop a rigorously spinadapted version of Mukherjee's statespecific multireference coupled cluster theory (SSMRCC, also known as MkMRCC) [U. S. Mahapatra, B. Datta, and D. Mukherjee, J. Chem. Phys. 110, 6171 (1999)] for reference spaces comprising openshell configurations. The principal features of our approach are as follows: (1) The wave operator Ω is written as Ω = ∑(μ)Ω(μ)φ(μ)>c(μ), where {φ(μ)} is the set of configuration state functions spanning a complete active space. (2) In contrast to the JeziorskiMonkhorst Ansatz in spinorbital basis, we write Ω(μ) as a power series expansion of cluster operators R(μ) defined in terms of spinfree unitary generators. (3) The operators R(μ) are either closedshelllike n holen particle excitations (denoted as T(μ)) or they involve valence (active) destruction operators (denoted as S(μ)); these latter type of operators can have activeactive scatterings, which can also carry the same active orbital labels (such S(μ)'s are called to have spectator excitations). (4) To simulate multiple excitations involving powers of cluster operators, we allow the S(μ)'s carrying the same active orbital labels to contract among themselves. (5) We exclude S(μ)'s with direct spectator scatterings. (6) Most crucially, the factors associated with contracted composites are chosen as the inverse of the number of ways the S(μ)'s can be joined among one another leading to the same excitation. The factors introduced in (6) have been called the automorphic factors by us. One principal thrust of this paper is to show that the use of the automorphic factors imparts a remarkable simplicity to the final amplitude equations: the equations consist of terms that are at most quartic in cluster amplitudes, barring only a few. In close analogy to the MkMRCC theory, the inherent linear dependence of the cluster amplitudes leading to redundancy is resolved by invoking sufficiency conditions, which are exact spinfree analogues of the spinorbital based MkMRCC theory. This leads to manifest sizeextensivity and an intruderfree formulation. Our formalism provides a relaxed description of the nondynamical correlation in presence of dynamical correlation. Pilot numerical applications to doublet systems, e.g., potential energy surfaces for the first two excited (2)A' states of asymmetric H(2)S(+) ion and the ground (2)Σ(+)state of BeH radical are presented to assess the viability of our formalism over an wide range of nuclear geometries and the manifest avoidance of intruder state problem.The Journal of Chemical Physics 02/2011; 134(5):054122. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Three recently developed multireference perturbation theories (PTs)—generalized Van Vleck PT (GVVPT), statespecific multireference PT (SSMRPT), 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 BeH2 system at various geometries, both in the ground and in the first excited singlet state. Furthermore, the ethylene twisting process is studied. Both Møller–Plesset (MP) and Epstein–Nesbet partition are used for MCPT and SSMRPT, while GVVPT uses MP partitioning. An important thrust in our comparative study is to ascertain the degree of interplay of dynamical and nondynamical correlation for both ground and excited states. The same basis set and the same set of orbitals are used in all calculations to keep artifactual differences away when comparing the results. Nonparallelity error is used as a measure of the performance of the respective theories. Significant differences among the three methods appear when an intruder state is present. Additionally, difficulties arise (a) in MCPT when the choice of a pivot determinant becomes problematic, and (b) in SSMRPT when there are small coefficients of the model function and there is implicit division by these coefficients, which generates a potential instability of the solutions. Ways to alleviate these latter shortcomings are suggested.The Journal of Chemical Physics 11/2009; 131(20):20410420410411. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we present a comprehensive account of an explicitly spinfree compact stateuniversal multireference coupled cluster (CC) formalism for computing the state energies of simple openshell systems, e.g., doublets and biradicals, where the target openshell states can be described by a few configuration state functions spanning a model space. The cluster operators in this formalism are defined in terms of the spinfree unitary generators with respect to the common closedshell component of all model functions (core) as vacuum. The spinfree cluster operators are either closedshelllike n holen particle excitations (denoted by T(mu)) or involve excitations from the doubly occupied (nonvalence) orbitals to the singly occupied (valence) orbitals (denoted by S(e)(mu)). In addition, there are cluster operators with exchange spectator scatterings involving the valence orbitals (denoted by S(re)(mu)). We propose a new multireference cluster expansion ansatz for the wave operator with the above generally noncommuting cluster operators which essentially has the same physical content as the JeziorskiMonkhorst ansatz with the commuting cluster operators defined in the spinorbital basis. The T(mu) operators in our ansatz are taken to commute with all other operators, while the S(e)(mu) and S(re)(mu) operators are allowed to contract among themselves through the spectator valence orbitals. An important innovation of this ansatz is the choice of an appropriate automorphic factor accompanying each contracted composite of cluster operators in order to ensure that each distinct excitation generated by this composite appears only once in the wave operator. The resulting CC equations consist of two types of terms: a "direct" term and a "normalization" term containing the effective Hamiltonian operator. It is emphasized that the direct term is almost quartic in the cluster amplitudes, barring only a handful of terms and termination of the normalization term depends on the valence rank of the effective Hamiltonian operator and the excitation rank of the cluster operators at which the theory is truncated. Illustrative applications are presented by computing the state energies of neutral doublet radicals and doublet molecular cations and ionization energies of neutral molecules and comparing our results with the other openshell CC theories, benchmark full CI results (when available) in the same basis, and the experimental results. Highly encouraging results show the efficacy of the method.The Journal of Chemical Physics 08/2009; 131(4):044124. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We present in this paper a sizeextensive formulation of a valence universal multireference coupled cluster (VUMRCC) theory which uses a general incomplete model space (IMS). The earlier formulations by Mukherjee [D. Mukherjee, Chem. Phys. Lett. 125 (1986) 207] led to sizeextensive Heff which was both connected and ‘closed’, thereby leading to sizeextensive energies. However, this necessitated abandoning the intermediate normalization (IN) for the valence universal waveoperator 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 Sqop which leads to excitations into the complementary model space by their action on at least one model function. The powers of Sqop 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. Sqop 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 Lqop=0, and Lop=0 for the transformed operator L=Ω1HΩ would be in conflict with Ωqop=1qop, 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 counterterms 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 waveoperator which never generates any powers of Sqop, which is closed. This ‘externally projected’ waveoperator does not need counterterms 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 VUMRCC equations for decreasing valence ranks are all satisfied by this new Ansatz for the waveoperator.Chemical Physics 01/2009; 356(1):5463. · 1.96 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this article, we present an explicitly spinfree compact coupled cluster (CC) theory for simple openshell systems, e.g., doublets, biradicals, which can be described either by a single openshell determinant or by a configuration state function (CSF) which corresponds to a single spatial configuration but is a linear combination of determinants with different spin allocations. A new cluster expansion Ansatz for the waveoperator is introduced, in which the spinfree cluster operators are either of the form of closedshelllike n holen particle excitations or contain valence excitations, which may involve exchange spectator scatterings. These latter type of operators are allowed to contract among themselves through the spectator orbitals. The novelty of the Ansatz is in the choice of a suitable automorphic factor accompanying each composite of noncommuting operators, ensuring that each such composite appears only once. The resulting CC equations consist of two types of terms: one is direct and the other is folded and the latter involves the effective Hamiltonian operator. We emphasize that while the direct term terminates exactly at the quartic power of the cluster amplitudes, termination of the folded term is dictated by the valence rank of the effective Hamiltonian operator, just as in the spinfree openshell CC theory with a normal ordered exponential Ansatz. Example applications are presented by computing the core and valenceionized state energies of H2O molecule and comparing the results with benchmark full CI results. The results show the efficacy of the method. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008International Journal of Quantum Chemistry 05/2008; 108(12):2211  2222. · 1.17 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We present in this Paper a brief account of a novel spinfree compact coupled cluster (CC) theory for simple openshell configurations, e.g. doublet and biradicals, which are not necessarily single determinants. A new cluster Ansatz for the waveoperator is introduced, in which the spinfree cluster operators are either of the type of closedshelllike n holen particle excitations or contain valence excitations, which may involve exchange spectator scatterings. The cluster operators with exchange valence spectator scatterings and the pure valence excitation operators are allowed to contract among themselves through the spectator orbitals. The novelty of the Ansatz is in the choice of a suitable automorphic factor accompanying each composite of noncommuting operators, ensuring that each such composite appears only once. This leads to CC equations which terminate exactly at the quartic power of the cluster amplitudes, reminiscent of the closedshell CC theory. As example applications, we compute the state energies of the ground state of OH and NH2 radicals with ccpVDZ basis set and assess the performance of the theory by comparing the results with the benchmark full CI results in the same basis set. The results show the power and the efficacy of the method.04/2008;  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we propose and apply an uncoupled approximation to the rigorous, sizeextensive statespecific multireference coupled cluster theory (SSMRCC), developed earlier by Mukherjee and coworkers [U.S. Mahapatra, B. Datta, D. Mukherjee, J. Chem. Phys. 110 (1999) 6171]. Both the parent formulation and the uncoupled approximant use the Jeziorski–Monkhorst Ansatz: Ω=∑μexp(Tμ)ϕμ〉〈ϕμ involving a different cluster operator exp(Tμ) acting on its corresponding model function ϕμ. The approximant presented in this paper builds on a preliminary formulation presented by us recently [THEOCHEM 79 (2006) 771]. The working equations of the SSMRCC, following a set of physically motivated sufficiency conditions, are characterized by certain projection amplitudes connecting each ϕμ to each virtual function χl, which is equated to zero. These equations have two types of terms: a ‘direct’ term where for each ϕμ only powers of Tμ appear, and a ‘coupling’ term where Tν (ν≠μ) also figures. In the uncoupled SSMRCC approximant (UCSSMRCC) we explore the possibility of avoiding the coupling term by approximating the coupling matrix element 〈χl∣exp(−Tμ)exp(Tν)∣ϕμ〉 by 〈χlexp(Tμ)exp(Tμ′(ν))ϕμ〉, where Tμ′(ν)s form the subset of the components of Tμ operators which has the same excitation structure of those operators Tν that give nontrivial contributions by their actions on ϕμ. Absence of the coupling terms leads to considerable simplifications of the working equations. Pilot molecular applications of the UCSSMRCC theory to the singlet states of CH2 and SiH2, which possess strongly multireference character and to the potential energy surface of the ground state of Li2 indicate the extreme closeness of the computed energies with those from the rigorous but more involved parent SSMRCC theory. This indicates the potentiality and the efficacy of the UCSSMRCC approximation.Chemical Physics 01/2008; 349(1):115120. · 1.96 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We describe in this paper a compact spinfree coupled cluster (CC) theory for simple openshell configurations, like doublets and biradicals, which are not necessarily single determinants. A new cluster Ansatz for the waveoperator is introduced, in which the cluster operators with direct valence spectator scatterings are replaced by closedshelllike single and double excitation operators. The cluster operators with exchange valence spectator scatterings and the pure valence excitation operators are allowed to contract among themselves through the spectator orbitals. The novelty of the Ansatz is in the choice of a suitable automorphic factor accompanying each composite of noncommuting operators, ensuring that each such composite appears only once. This leads to CC equations which terminate exactly at the quartic power of the cluster amplitudes, reminiscent of the closedshell CC theory. As a pilot example application, we compute the state energy of the ground state of the Fluorine radical with three different basis sets, and assess the performance of the theory by comparing with the benchmark full CI result in the same basis sets. The results show the power and the efficacy of the method.01/2007;  [Show abstract] [Hide abstract]
ABSTRACT: We present and implement in this paper a novel spinfree valenceuniversal multireference coupled cluster (VUMRCC) formalism for energy differences which can capture orbital relaxation and correlation relaxation to all orders. Unlike in the traditional normal ordered cluster Ansatz for computing energy differences, this cluster expansion formalism allows contractions between various valence excitation operators with valence spectator lines. These contractions simulate the orbital relaxation and correlation relaxation effects for the ionized/excited states via Thoulesslike exponential type of operators. Generally such operators are noncommuting. To ensure that each distinct excitation generated by contracted composites formed by these operators appear only once in the waveoperators, the factors accompanying these composites have to be judiciously chosen. Hence, the combinatoric factors accompanying such contracted composites are not taken to be 1/n! for nthpower, but rather the inverse of the automorphic factor (the number of ways the n operators can be connected in various permutations generating the same composite). It is shown that this Ansatz leads to a set of VUMRCC equations for the valence cluster amplitudes, in which all the cluster operators are attached to the hamiltonian by at least one nonspectator line (a strongly connected series). The series is thus terminating at the quartic power. Illustrative applications are presented by computing electron affinity of neutral doublet radicals (viz., NH2, OH, F, BO and CN), where the orbital relaxation effect attendant on the anion formation is considerable. Several basissets capable of describing the anions have been studied. It has been found that augccpVTZ basis gives the best overall results, while augccpVQZ overestimates the electron affinity, presumably because of an imbalance in describing the neutral radicals. The method performs consistently much better then the one with the traditional normal ordered Ansatz.Chemical Physics 01/2006; 329(1):290306. · 1.96 Impact Factor
Publication Stats
92  Citations  
40.52  Total Impact Points  
Top Journals
Institutions

2012–2014

Johannes GutenbergUniversität Mainz
 Institute of Physical Chemistry
Mayence, RheinlandPfalz, Germany 
St. Xavier's College, Kolkata
 Department of Physics
Kolkata, Bengal, India


2013

Academy of Sciences of the Czech Republic
 Ústav fyzikální chemie J. Heyrovského
Praha, Hlavni mesto Praha, Czech Republic


2011

University of Waterloo
 Department of Chemistry
Waterloo, Quebec, Canada


2008–2009

Indian Association for the Cultivation of Science
 • Department of Physical Chemistry
 • Raman Center for Atomic, Molecular and Optical Sciences
Calcutta, Bengal, India
