Reactivity descriptors: conceptual and computational developments - Pal, Sourav (International Conference on Computational Methods in Sciences and Engineering (ICCMSE 2005), 2005)

Role of substituents on the reactivity and electron density profile of diimine ligands: a density functional theory based study - Kulkarni, Bhakti S.; Mishra, Deepti; Pal, Sourav (Journal of Chemical Sciences, 2013)
In this paper, we study the reactivity of diimines like 2, 2(')-bipyridine, 1, l0-phenanthroline and 1, 2, 4-triazines using density-based reactivity descriptors. We discuss the enhancement or diminution in the reactivity of these ligands as a function of two substituent groups, namely methyl (-CH3) group and phenyl (-C6H5) group. The global reactivity descriptors explain the global affinity and philicity of these ligands, whereas the local softness depicts the particular site selectivity. The inter-molecular reactivity trends for the same systems are analysed through the philicity and group philicity indices. The sigma-donor character of these ligands is quantified with the help of electron density profile. In addition, the possible strength of interaction of these ligands with metal ions is supported with actual reaction energies of Ru-L complexes.
Keywords: 2; 2 `-bipyridine; DFT; diimine; Reactivity descriptors; Ru-ligand interaction; substituent effects

Relativistic equation-of-motion coupled-cluster method: application to closed-shell atomic systems - Pathak, Himadri; Sahoo, B. K.; Das, B. P.; Vaval, Nayana; Pal, Sourav (Physical Review Applied, 2014)
We report our successful implementation of the relativistic equation-of-motion coupled-cluster (EOMCC) method. This method is employed to compute the principal ionization potentials (IPs) of closed-shell rare-gas atoms, He-like ions, Be-like ions, along with Na+, Al+, K+, Be, andMg. Four-component Dirac spinors are used in the calculations, and the one-and two-electron integrals are evaluated using the Dirac-Coulomb Hamiltonian. Our results are in excellent agreement with available measurements, which are taken from the National Institute of Science and Technology database. The accuracies of the calculations are estimated to be within one half of a percent for He-like and Be-like ions and 1% for the heavier systems. We also present results using the second-order many-body perturbation theory and random-phase approximation in the EOMCC framework. These results are compared with those of EOMCC at the level of single and double excitations in order to assess the role of the electron correlation effects in the intermediate schemes considered in our calculations.

Relativistic equation-of-motion coupled-cluster method for the double-ionization potentials of closed-shell atoms - Pathak, Himadri; Ghosh, Aryya; Sahoo, B. K.; Das, B. P.; Vaval, Nayana; Pal, Sourav (Physical Review A, 2014)

Relativistic equation-of-motion coupled-cluster method for the ionization problem: application to molecules - Pathak, Himadri; Sasmal, Sudip; Nayak, Malaya K.; Vaval, Nayana; Pal, Sourav (Physical Review A, 2014)
We report the implementation of the four-component spinor relativistic equation-of-motion (EOM) coupled-cluster method within the single- and double-excitation approximation to calculate the ionization potential of molecules. We have applied this method to calculate vertical ionization potentials of the molecules XH (X = F, Cl, Br, I) along with Cl-2 and Br-2 in their closed-shell configuration. We have also presented intermediate results using the second-order many-body perturbation-theory level in the EOM framework to understand the role of electron correlation. All the calculated values are compared with the available experimental results. Our results are found to be in good agreement with sophisticated experiments, and relative deviation of less than 1% is achieved for all the considered systems.

Relativistic spectroscopy of plasma-embedded Li-like systems with screening effects in two-body Debye potentials - Das, Madhulita; Sahoo, B. K.; Pal, Sourav (Journal of Physics B-Atomic Molecular and Optical Physics, 2014)
The spectroscopic properties of Li atoms and Li-like Ca and Ti ions in the plasma environment are investigated using a relativistic coupled-cluster (RCC) method. Assuming that the plasma is of low density and very hot, we consider the Debye model with two approximations to account for the screening effects: (i) in the nuclear potential alone and (ii) in both the nuclear and the electron-electron interaction potentials. Also, calculations for the energies and the lifetimes of the atomic states are carried out for plasma-free systems to check their accuracy, after which they are investigated in the plasma environment. It is observed that screenings in the electron-electron interaction potentials stabilize the systems more than when the screenings are present only in the nuclear potential. Similarly, the blue and red shifts in the Delta n = 0 and Delta n not equal 0 transition lines (with the principal quantum number n) of the Li-like ions observed in the (i) approximation are altered in the (ii) approximation. The level crossings among the energy levels are observed for large screening effects and are found to be prominent in the states of higher orbital angular momentum. The lifetimes of many low-lying states of the allowed transitions are estimated by considering different plasma screening strengths.
Keywords: atomic Spectroscopy; Debye model; relativistic method

Reactivity and catalytic activity of hydrogen atom chemisorbed silver clusters - Manzoor, Dar; Pal, Sourav (Journal of Physical Chemistry A, 2015)
Metal clusters of silver have attracted recent interest of researchers as a result of their potential in different,catalytic applications and low Cost. However, due to the completely filled d orbital and very high first ionization potential of the silver atom, the silver-based catalysts interact very weakly with the reacting molecules. In the current work, density functional theory calculations were carried out to investigate the effect of hydrogen atom chemisorption. On the reactivity and catalytic properties of inert silver clusters Our results affirm that the hydrogen atom chemisorption leads to enhancement the binding energy of the adsorbed O-2 molecule on the inert silver clusters. The increase in the binding energy is also characterized by the decrease in the Ag-O and increase in the O-O bond lengths in the case of the AgnH Silver clusters. Pertinent to the increase in the O-O bond length, a. significant red shift in the O-O Stretching frequency is. also noted in the case,of the AgnH silver clusters. Moreover, the hydrogen atom chemisorbed silver clusters show low reaction barriers and heat Of formation of the final products for the,environmentally important CO oxidation reaction as compared to the parent catalytically inactive clusters The obtained results were compared with those of the corresponding gold and hydrogen atom chemisorbed gold clusters obtained at the same level of theory. It is expected the current computational study will provide key insights for future advances in the design of efficient nanosilver-based catalysts through the adsorption of a small atom or a ligand.

Relativistic equation-of-motion coupled-cluster investigation of the trends of single and double ionization potentials in the He and Be isoelectronic systems - Pathak, Himadri; Sahoo, B. K.; Sengupta, Turbasu; Das, B. P.; Vaval, Nayana; Pal, Sourav (Journal of Physics B-Atomic Molecular and Optical Physics, 2015)
We employ a four-component spinor relativistic equation-of-motion coupled-cluster (EOMCC) method within the single-and double-excitation approximation to calculate the single ionization potentials (IPs) and double ionization potentials (DIPs) of the He and Be isoelectronic sequences up to Ne. The obtained results are compared with the available results from the National Institute of Standards and Technology (NIST) database to test the performance of the EOMCC method. We also present intermediate results at different levels of approximations in the EOMCC framework to gain insight of the effect of electron correlation. Furthermore, we investigate the dependence of the IPs and DIPs of these ions on the ionic charge and observe that these follow parabolic trends. Similarities between the trends of IPs and DIPs in both the classes of considered systems are categorically demonstrated.
Keywords: coupled-cluster method; double ionization potentials; equation-of-motion theory

Relativistic extended coupled cluster method for magnetic hyperfine structure constant - Sasmal, Sudip; Pathak, Himadri; Nayak, Malaya K.; Vaval, Nayana; Pal, Sourav (Physical Review A, 2015)

Radical attached aluminum nanoclusters: an alternative way of cluster stabilization - Sengupta, Turbasu; Pal, Sourav (Physical Chemistry Chemical Physics, 2016)
The stability and electronic structure of radical attached aluminum nanoclusters are investigated using density functional theory (DFT). A detailed investigation shows good correlation between the thermodynamic stability of radical attached clusters and the stability of the attached radical anions. All other calculated parameters like HOMO-LUMO gap and charge transfer are also found to be consistent with the observed thermodynamic stabilities of the complexes. Investigation of the electronic structure of radical attached complexes further shows the presence of jellium structures within the core similar to the ligated clusters. Comparison with available experimental and theoretical data also proves the validity of superatomic complex theory for the radical attached clusters as well. Based on the evaluated thermodynamic parameters, selected radical attached clusters are observed to be more thermodynamically stable in comparison with experimentally synthesized ligated clusters. Stabilization of small metal clusters is one of the greatest challenges in current cluster science and the present investigation confirms the fact that radical attached clusters can provide a viable alternative to ligated clusters in the future.

Relativistic coupled-cluster study of RaF as a candidate for the parity- and time-reversal-violating interaction - Sasmal, Sudip; Pathak, Himadri; Nayak, Malaya K.; Vaval, Nayana; Pal, Sourav (Physical Review A, 2016)
We have employed both the Z-vector method and the expectation-value approach in the relativistic coupled-cluster framework to calculate the scalar-pseudoscalar (S-PS) P, T-odd interaction constant W-s and the effective electric field E-eff experienced by the unpaired electron in the ground electronic state of RaF. Further, the magnetic hyperfine structure constants of Ra-223 in RaF and Ra-223(+) are also calculated and compared with the experimental values wherever available to judge the extent of the accuracy obtained with the employed methods. The outcome of our study reveals that the Z-vector method is superior to the expectation-value approach in terms of accuracy obtained for the calculation of ground-state property. The Z-vector calculation shows that RaF has a high Eeff (52.5 GV/cm) and W-s (141.2 kHz), which makes it a potential candidate for the electric dipole moment of the electron (eEDM) experiment. An estimation of uncertainty associated with our final results is made, and it is found that it lies below 10%.

Relativistic equation-of-motion coupled-cluster method for the electron attachment problem - Pathak, Himadri; Sasmal, Sudip; Nayak, Malaya K.; Vaval, Nayana; Pal, Sourav (Computational and Theoretical Chemistry, 2016)
The article considers the successful implementation of relativistic equation-of-motion coupled cluster method for the electron attachment problem (EA-EOMCC) at the level of single- and double- excitation approximation. The implemented relativistic EA-EOMCC method is employed to calculate ionization potential values of alkali metal atoms (Li, Na, K, Rb, Cs, Fr) and the vertical electron affinity values of LiX (X = H, F, Cl, Br), NaY (Y = H, F, Cl) starting from their closed-shell configuration. Both four component and exact two-component calculations are done for all the opted systems. Further, we have shown the effect of spin-orbit interaction considering the atomic systems. The results of our atomic calculations are compared with the values from the NIST database and the results are found to be very accurate (<1%). (C) 2015 Elsevier B.V. All rights reserved.

Relativistic coupled-cluster investigation of parity (P) and time-reversal (T) symmetry violations in HgF - Talukdar, Kaushik; Nayak, Malaya K.; Vaval, Nayana; Pal, Sourav (Journal of Chemical Physics, 2019)
We employ the Z-vector method in the four-component relativistic coupled-cluster framework to calculate the parity (P) and time-reversal (T) symmetry violating scalar-pseudoscalar nucleus-electron interaction constant (W-s), the effective electric field (E-eff) experienced by the unpaired electron, and the nuclear magnetic quadrupole moment-electron interaction constant (W-M) in the open-shell ground electronic state of HgF. The molecular frame dipole moment and the magnetic hyperfine structure (HFS) constant of the molecule are also calculated at the same level of theory. The outcome of our study is that HgF has a high value of E-eff (115.9 GV/cm), W-s (266.4 kHz), and W-M (3.59 x 10(33) Hz/e cm(2)), which shows that it can be a possible candidate for the search of new physics beyond the standard model. Our results are in good agreement with the available literature values. Furthermore, we investigate the effect of the basis set and the virtual energy functions on the computed properties. The role of the high-energy virtual spinors is found to be significant in the calculation of the HFS constant and the P,T-odd interaction coefficients. Published under license by AIP Publishing.

Relativistic coupled-cluster study of BaF in search of CP violation - Talukdar, Kaushik; Nayak, Malaya K.; Vaval, Nayana; Pal, Sourav (Journal of Physics B-Atomic Molecular and Optical Physics, 2020)
BaF is one of the potential candidates for the experimental search of the electric dipole moment of the electron (eEDM). The NL-eEDM collaboration is building a new experimental set up to measure the eEDM using the BaF molecule (The NL-eEDM collaboration, 2018 Eur. Phys. J. D 72: 197). To analyze the results of such an experiment, one would require the accurate value of the molecular P, T-odd interaction parameters that cannot be measured from any experiment. In this work, we report the precise value of the P, T-odd interaction parameters of the BaF molecule obtained from the four-component relativistic coupled-cluster calculations. We also calculate the hyperfine structure (HFS) constants of the same molecule to assess the reliability of the reported molecular parameters. The calculated HFS constants show good agreement with the available experimental values. Further, the systematic effects of electron-correlation along with the roles of inner-core electrons and the virtual energy functions in the calculation of the studied properties of BaF are investigated.
Keywords: electric dipole moment of the electron; electron-correlation; Relativistic effects

Relativistic double-ionization equation-of-motion coupled-cluster method: application to low-lying doubly ionized states - Pathak, Himadri; Sasmal, Sudip; Talukdar, Kaushik; Nayak, Malaya K.; Veval, Nayana; Pal, Sourav (Journal of Chemical Physics, 2020)
This article deals with the extension of the relativistic double-ionization equation-of-motion coupled-cluster (DI-EOMCC) method [H. Pathak et al. Phys. Rev. A 90, 010501(R) (2014)] for the molecular systems. The Dirac-Coulomb Hamiltonian with four-component spinors is considered to take care of the relativistic effects. The implemented method is employed to compute a few low-lying doubly ionized states of noble gas atoms (Ar, Kr, Xe, and Rn) and Cl-2, Br-2, HBr, and HI. Additionally, we presented results with two intermediate schemes in the four-component relativistic DI-EOMCC framework to understand the role of electron correlation. The computed double ionization spectra for the atomic systems are compared with the values from the non-relativistic DI-EOMCC method with spin-orbit coupling [Z. Wang et al. J. Chem. Phys. 142, 144109 (2015)] and the values from the National Institute of Science and Technology (NIST) database. Our atomic results are found to be in good agreement with the NIST values. Furthermore, the obtained results for the molecular systems agree well with the available experimental values.

Role of electron correlation in the P, T-odd effects of CdH: a relativistic coupled-cluster investigation - Talukdar, Kaushik; Nayak, Malaya K.; Vaval, Nayana; Pal, Sourav (Physical Review A, 2020)
We investigate the parity (P) and time-reversal (T) symmetry violating effects in the CdH molecule and perform the relativistic coupled-cluster calculation of the molecular parameters-E-eff, W-s, and W-M-related to the electric dipole moment of electron (eEDM) interaction, the scalar-pseudoscalar (S-PS) nucleus-electron neutral current coupling, and the nuclear magnetic quadrupole moment (MQM) interaction with electrons, respectively. We also compute the molecular dipole moment and the magnetic hyperfine structure coupling constant of CdH. The values of E-eff, W-s, and W-M obtained by us in the said molecule are 12.2 GV/cm, 14.0 kHz, and 0.82 x 10(33) Hz/e cm(2), respectively, within an uncertainty of 10%. Furthermore, we study the trend of electron-correlation in the computed properties of CdH and that of the P, T-odd parameters in the group-12 monohydrides (i.e., ZnH, CdH, and HgH).

Resonance study: effect of partial triples excitation using complex absorbing potential-based Fock-space multi-reference coupled cluster - Jana, Irina; Basumallick, Suhita; Pal, Sourav; Vaval, Nayana (International Journal of Quantum Chemistry, 2021)
Resonances are metastable states with finite lifetime. They play important role in physics, chemistry and biology. The theoretical calculation of resonance state is a challenging problem. In this paper we have studied the shape resonance of Be, Mg, N-2 and CO. We have used correlated independent particle approximation to the Fock space multi-reference coupled cluster singles-doubles with third-order triples (CAP-CIP-FSMRCCSD(T)) method augmented by complex absorption potential. The resonance energy and decay widths are obtained by solving a non-Hermitian eigen-value problem within FSMRCC framework. The effects of the lowest order triples on the resonance energy and decay are studied.
Keywords: complex absorbing potential; electron affinity; Fock‐ negative ion resonance; partial triples; space MRCC

Relativistic coupled-cluster study of SrF for low-energy precision tests of fundamental physics - Talukdar, Kaushik; Buragohain, Haimyapriya; Nayak, Malaya K. K.; Vaval, Nayana; Pal, Sourav (Theoretical Chemistry Accounts, 2023)
SrF, being a laser-coolable molecule, can be an interesting system for spectroscopic tests of fundamental physics. We present an electronic structure study of this molecule within the four-component relativistic coupled-cluster singles and doubles (RCCSD) framework and employ the RCCSD-based methods to compute its molecular-frame dipole moment and core properties such as hyperfine structure coupling constant and molecular P, T-odd electronic structure parameters that are of great importance for the high-precision tests of fundamental physics. The impact of basis set size, Hamiltonian and nuclear model on the property calculation of SrF is also investigated. The computed results are in good agreement with the available experimental values. The present study shows that the SrF molecule could be useful for high-precision molecular experiments to explore physics beyond the Standard Model of elementary particles.
Keywords: Coupled cluster theory; CP violation; Hyperfine structure; Molecular spectroscopy; Relativistic effects

Relativistic extended-coupled-cluster calculations of P , T -odd sensitivity parameters for diatomic molecules - Talukdar, Kaushik; Nayak, Malaya K.; Vaval, Nayana; Pal, Sourav (Journal of Chemical Theory and Computation, 2025)
We demonstrate the first application of the four-component relativistic extended-coupled-cluster (ECC) method, a variational approach, to determine the P , T -odd molecular electronic structure parameters necessary for high-precision spectroscopic measurements on ultracold molecules. We calculate the P , T -odd sensitivity parameters for two moderately heavy, laser-coolable diatomic molecules (SrH and SrF), as well as two relatively lighter open-shell molecules (CaH and CaF) in their ground electronic state, 2 Sigma 1/2. The hyperfine structure constants of 87Sr in the SrF and SrH molecules are also computed and compared with available experimental results to assess the accuracy of our calculations. Furthermore, we examine the roles of electron correlation, relativity, basis set, and virtual spinors in ECC calculations of the sensitivity parameters. Our study reveals that the ECC method is a reliable technique for studying P , T -odd properties of diatomic molecules such as CaH, CaF, SrH and SrF, yielding results in very good agreement with those obtained using two widely employed analytic approaches: the Z-vector technique and the linear expectation-value method within the relativistic single-reference coupled-cluster singles and doubles framework.