Speaker
Description
The investigation on high-precision calculations of molecular ions emerges as a captivating and fascinating domain of research. The meticulous exploration of molecular ions necessitates a comprehensive understanding of their structural, electronic and dynamic properties. In a molecular system, unlike in an atomic system, describing nuclear motion is significantly more complicated due to the constraints on its movement. Consequently, calculations beyond the Born-Oppenheimer approximation become exceedingly intricate. Apart from the approximation method, such as coupled-cluster, density functional, perturbation theory etc., the Ritz variational method turns out to be one of the most efficient methods to accurately determine structural properties of a three-body molecular system [1-4]. In this work, we have studied the structural properties of various symmetric and asymmetric molecular three-body systems, such as H$_2^+$, D$_2^+$, T$_2^+$, HD+, DT+ (and their muonic substitutions) etc., using the trial wave function expanded in explicitly correlated Hyllerass type basis set of the form: $\Psi\left(r_1,r_2,r_{12}\right)=\left(1+k{\hat{P}}_{12}\right)\sum_{i=1}^{N}C_ir_1^{l_i}r_2^{m_i}r_{12}^{n_i}\ exp\left(-\alpha_ir_1-\beta_ir_2-\gamma_ir_{12}\right)$, where $\left(r_1,r_2,r_{12}\right)$ are the relative coordinates, ${\hat{P}}_{12}$ is the two-particle permutation operator, $\left(l_i,m_i,n_i\right)$ and $\left(\alpha_i,\beta_i,\gamma_i\right)$ are basis set parameters and non-linear exponents, $k=+1 (-1)$ is for symmetric singlet (triplet) and $k=0$ is for an asymmetric system. Further, we consider an additional large parameter M in the power of inter-nuclear distance $r_{12}$ to ensure that the factor $r_{12}^{n_i+M}exp\left(-\gamma_ir_{12}\right)$ replicates the notion of Gaussian profile essential for capturing the localized nature of nuclear motion. The stabilization method [5] is utilized to accurately determine the energy eigenvalues and geometrical quantities (such as expectation values of inter-nuclear distance, nuclear-particle separation, corresponding angles, cusps etc.) of ground and some low-lying singly excited states, as well as continuum embedded Feshbach resonance states. Moreover, we have tried to expand the present explicitly correlated method to assess its viability in investigating four-body molecular systems, such as Ps$_2$ and H$_2$ molecules, which offer intriguing characteristics unique to such systems.
References:
1. S. Mondal, A. Sadhukhan, T. K. Mukhopadhyay, M. Pawlak and J. K. Saha; Physica Scripta 98, 015408 (2022)
2. S. Majumdar and A. K. Roy; Frontiers in Chemistry 10, 926916 (2022)
3. A. Ghosal and A. K. Roy; Molecular Physics 120, e1983056 (2022)
4. A. Ghosal, T. Mandal and A. K. Roy; International Journal of Quantum Chemistry 118, e25708 (2018)
5. J. K. Saha and T. K. Mukherjee; Physical Review A 80, 022513 (2009)
