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

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).

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.