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Chen BJ, Pradhan E, Nooijen M, Zeng T. Adiabat-to-Diabat Angle in Seam Space: Renner-Teller-Type and Pseudo-Jahn-Teller-Type Problems. Chemphyschem 2024; 25:e202400130. [PMID: 38427966 DOI: 10.1002/cphc.202400130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2024] [Revised: 02/29/2024] [Accepted: 03/01/2024] [Indexed: 03/03/2024]
Abstract
In this study, we examine the adiabat-to-diabat (ATD) angles for trajectories in 2-dimensional vibrational subspace of the seam space of two degenerate states. In circulating around the tangential touching degeneracy center, the ATD angle is changed by2 π ${2\pi }$ or 0, similar to the Renner-Teller problem and the pseudo-Jahn-Teller problem, respectively. These ATD angle profiles may be indistinguishable from those of circulating multiple conical intersections or a pseudo-Jahn-Teller center. Methods to discern those seemingly indistinguishable cases are proposed. A sharp zigzag variation of the ATD angle is seen as a feature for trajectories that graze a pseudo-Jahn-Teller-type tangential touching center, in contrast to the monotonic steep variation for grazing a conical intersection or a Renner-Teller-type tangential touching center.
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Affiliation(s)
- Benny Jun Chen
- Department of Chemistry, University of Waterloo, Waterloo, ON, N2 L3G1, Canada
| | - Ekadashi Pradhan
- Department of Chemistry, York University, Toronto, Ontario, M3 J1P3, Canada
| | - Marcel Nooijen
- Department of Chemistry, University of Waterloo, Waterloo, ON, N2 L3G1, Canada
| | - Tao Zeng
- Department of Chemistry, York University, Toronto, Ontario, M3 J1P3, Canada
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2
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Sah MK, Mukherjee S, Saha S, Naskar K, Adhikari S. Photoelectron spectra of benzene: Can path dependent diabatic surfaces provide unique observables? J Chem Phys 2023; 159:244116. [PMID: 38153145 DOI: 10.1063/5.0177186] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2023] [Accepted: 11/30/2023] [Indexed: 12/29/2023] Open
Abstract
While carrying out Beyond Born-Oppenheimer theory based diabatization, the solutions of adiabatic-to-diabatic transformation equations depend on the paths of integration over two-dimensional cross-sections of multi-dimensional space of nuclear degrees of freedom. It is shown that such path-dependent solutions leading to diabatic potential energy surface matrices computed along any two different paths are related through an orthogonal matrix, and thereby, those surface matrices should provide unique observables. While exploring the numerical validity of the theoretical framework, we construct diabatic Hamiltonians for the five low-lying electronic states (X̃2E1g, B̃2E2g, and C̃2A2u) of benzene radical cation (C6H6+) along three different approaches of contour integration over two dimensional nuclear planes constituted by seven non-adiabatically active normal modes. Three different diabatic surface matrices are further employed to generate the photoelectron spectra of the benzene molecule (C6H6). It is interesting to note that the spectral peak positions and intensity patterns for all three cases are almost close to each other and also exhibit very good agreement with the experimental results.
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Affiliation(s)
- Mantu Kumar Sah
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Soumya Mukherjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Swagato Saha
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Koushik Naskar
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Satrajit Adhikari
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
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3
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Mukherjee S, Hazra S, Ghosh S, Mukherjee S, Adhikari S. Trajectory Surface Hopping vs. Quantum Scattering Calculations on D+ + H2 and H + H2+ Reactions using Ab Initio Surfaces and Couplings. Chem Phys 2022. [DOI: 10.1016/j.chemphys.2022.111588] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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4
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Mukherjee S, Ravi S, Dutta J, Sardar S, Adhikari S. Beyond Born-Oppenheimer based diabatic surfaces of 1,3,5-C 6H 3F 3+ to generate the photoelectron spectra using time-dependent discrete variable representation approach. Phys Chem Chem Phys 2022; 24:2185-2202. [PMID: 35006221 DOI: 10.1039/d1cp04733g] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this article, Beyond Born-Oppenheimer (BBO) treatment is implemented to construct diabatic potential energy surfaces (PESs) of 1,3,5-C6H3F3+ over a series [eighteen (18)] of two-dimensional (2D) nuclear planes constituted with eleven normal modes (Q2, Q9x, Q9y, Q13x, Q13y, Q18x, Q18y, Q10x, Q10y, Q12x and Q12y) to include all possible nonadiabatic interactions among six coupled electronic states (X̃2E'', , B̃2E' and ). We had formulated explicit expressions of adiabatic to diabatic transformation (ADT) equations [S. Mukherjee, J. Dutta, B. Mukherjee, S. Sardar and S. Adhikari, J. Chem. Phys., 2019, 150, 064308] for the same system forming six state sub-Hilbert space and at present, these ADT equations are solved by incorporating MRCI level ab initio adiabatic PESs and CP-MCSCF calculated nonadiabatic coupling terms (NACTs) to derive diabatic PESs and couplings. Such single-valued, smooth, symmetric and continuous diabatic surface matrices are utilized to carry out multi-state multi-mode nuclear dynamics with the help of time-dependent discrete variable representation (TDDVR) methodology to compute the photoelectron (PE) spectra of 1,3,5-C6H3F3. Our theoretically calculated spectra for X̃2E'', and states using BBO treatment and TDDVR dynamics show peak by peak correspondence with the experimental results as well as better than the findings of the multi-configuration time-dependent Hartree (MCTDH) method.
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Affiliation(s)
- Soumya Mukherjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata - 700032, India.
| | - Satyam Ravi
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata - 700032, India. .,School of Advance Science and Languages, VIT Bhopal University, Bhopal - 466114, India
| | - Joy Dutta
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata - 700032, India.
| | - Subhankar Sardar
- Department of Chemistry, Bhatter College, Dantan, Paschim Medinipur - 721426, India
| | - Satrajit Adhikari
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata - 700032, India.
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5
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Mukherjee S, Ravi S, Naskar K, Sardar S, Adhikari S. A beyond Born–Oppenheimer treatment of C6H6+ radical cation for diabatic surfaces: Photoelectron spectra of its neutral analog using time-dependent discrete variable representation. J Chem Phys 2021; 154:094306. [DOI: 10.1063/5.0040361] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Soumya Mukherjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Satyam Ravi
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Koushik Naskar
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Subhankar Sardar
- Department of Chemistry, Bhatter College, Dantan, Paschim Medinipur 721426, India
| | - Satrajit Adhikari
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
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6
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Dutta J, Mukherjee S, Naskar K, Ghosh S, Mukherjee B, Ravi S, Adhikari S. The role of electron-nuclear coupling on multi-state photoelectron spectra, scattering processes and phase transitions. Phys Chem Chem Phys 2020; 22:27496-27524. [PMID: 33283826 DOI: 10.1039/d0cp04052e] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present first principle based beyond Born-Oppenheimer (BBO) theory and its applications on various models as well as realistic spectroscopic and scattering processes, where the Jahn-Teller (JT) theory is brought in conjunction with the BBO approach on the phase transition of lanthanide complexes. Over one and half decades, our development of BBO theory is demonstrated with ab initio calculations on representative molecules of spectroscopic interest (NO2 radical, Na3 and K3 clusters, NO3 radical, C6H6+ and 1,3,5-C6H3F3+ radical cations) as well as triatomic reactive scattering processes (H+ + H2 and F + H2). Such an approach exhibits the effect of JT, Renner-Teller (RT) and pseudo Jahn-Teller (PJT) type of interactions. While implementing the BBO theory, we generate highly accurate diabatic potential energy surfaces (PESs) to carry out quantum dynamics calculation and find excellent agreement with experimental photoelectron spectra of spectroscopic systems and cross-sections/rate constants of scattering processes. On the other hand, such electron-nuclear couplings incorporated through JT theory play a crucial role in dictating higher energy satellite transitions in the dielectric function spectra of the LaMnO3 complex. Overall, this article thoroughly sketches the current perspective of the BBO approach and its connection with JT theory with various applications on physical and chemical processes.
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Affiliation(s)
- Joy Dutta
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India.
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7
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Mukherjee B, Naskar K, Mukherjee S, Ravi S, Shamasundar KR, Mukhopadhyay D, Adhikari S. Beyond Born-Oppenheimer constructed diabatic potential energy surfaces for F + H 2 reaction. J Chem Phys 2020; 153:174301. [PMID: 33167635 DOI: 10.1063/5.0021885] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
First principles based beyond Born-Oppenheimer theory has been implemented on the F + H2 system for constructing multistate global diabatic Potential Energy Surfaces (PESs) through the incorporation of Nonadiabatic Coupling Terms (NACTs) explicitly. The spin-orbit (SO) coupling effect on the collision process of the F + H2 reaction has been included as a perturbation to the non-relativistic electronic Hamiltonian. Adiabatic PESs and NACTs for the lowest three electronic states (12A', 22A', and 12A″) are determined in hyperspherical coordinates as functions of hyperangles for a grid of fixed values of the hyperradius. Jahn-Teller (JT) type conical intersections between the two A' states translate along C2v and linear geometries in F + H2. In addition, A' and A″ states undergo Renner-Teller (RT) interaction at collinear configurations of this system. Both JT and RT couplings are validated by integrating NACTs along properly chosen contours. Subsequently, we have solved adiabatic-to-diabatic transformation (ADT) equations to evaluate the ADT angles for constructing the diabatic potential matrix of F + H2, including the SO coupling terms. The newly calculated diabatic PESs are found to be smooth, single-valued, continuous, and symmetric and can be invoked for performing accurate scattering calculations on the F + H2 system.
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Affiliation(s)
- Bijit Mukherjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | - Koushik Naskar
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | - Soumya Mukherjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | - Satyam Ravi
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | - K R Shamasundar
- Department of Chemical Science, Indian Institute of Science Education and Research, Mohali, India
| | | | - Satrajit Adhikari
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
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8
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Kalemos A. The nature of the chemical bond in NO3, neutral and anion. Theor Chem Acc 2020. [DOI: 10.1007/s00214-020-2563-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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9
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Naskar K, Mukherjee S, Mukherjee B, Ravi S, Mukherjee S, Sardar S, Adhikari S. ADT: A Generalized Algorithm and Program for Beyond Born–Oppenheimer Equations of “N” Dimensional Sub-Hilbert Space. J Chem Theory Comput 2020; 16:1666-1680. [DOI: 10.1021/acs.jctc.9b00948] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Koushik Naskar
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Soumya Mukherjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Bijit Mukherjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Satyam Ravi
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Saikat Mukherjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Subhankar Sardar
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
- Department of Chemistry, Bhatter College, Dantan, Paschim Medinipur 721426, India
| | - Satrajit Adhikari
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
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10
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Mukherjee B, Naskar K, Mukherjee S, Ghosh S, Sahoo T, Adhikari S. Beyond Born–Oppenheimer theory for spectroscopic and scattering processes. INT REV PHYS CHEM 2019. [DOI: 10.1080/0144235x.2019.1672987] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Bijit Mukherjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, India
| | - Koushik Naskar
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, India
| | - Soumya Mukherjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, India
| | - Sandip Ghosh
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, India
| | - Tapas Sahoo
- Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada
| | - Satrajit Adhikari
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, India
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11
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Mukherjee S, Mukherjee B, Sardar S, Adhikari S. Extended Born-Oppenheimer equations for non-Abelian situations: A study on NO3 radical and 1,3,5-C6H3F3+ radical cation. COMPUT THEOR CHEM 2019. [DOI: 10.1016/j.comptc.2019.03.011] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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12
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Mukherjee S, Dutta J, Mukherjee B, Sardar S, Adhikari S. Conical intersections and nonadiabatic coupling terms in 1,3,5-C6H3F3+: A six state beyond Born-Oppenheimer treatment. J Chem Phys 2019; 150:064308. [DOI: 10.1063/1.5064519] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Soumya Mukherjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata
700032, India
| | - Joy Dutta
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata
700032, India
| | - Bijit Mukherjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata
700032, India
| | - Subhankar Sardar
- Department of Chemistry, Bhatter College, Dantan, Paschim Medinipur 721426,
India
| | - Satrajit Adhikari
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata
700032, India
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13
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Mukherjee B, Mukherjee S, Sardar S, Shamasundar K, Adhikari S. A beyond Born-Oppenheimer treatment of five state molecular system NO3 and the photodetachment spectra of its anion. Chem Phys 2018. [DOI: 10.1016/j.chemphys.2018.09.017] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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14
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Mukherjee S, Mukherjee B, Dutta J, Sardar S, Adhikari S. Topological Effects in Vibronically Coupled Degenerate Electronic States: A Case Study on Nitrate and Benzene Radical Cation. ACS OMEGA 2018; 3:12465-12475. [PMID: 31457977 PMCID: PMC6644592 DOI: 10.1021/acsomega.8b01648] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/13/2018] [Accepted: 09/12/2018] [Indexed: 06/10/2023]
Abstract
We carry out detailed investigation for topological effects of two molecular systems, NO3 radical and C6H6 + (Bz+) radical cation, where the dressed adiabatic, dressed diabatic, and adiabatic-via-dressed diabatic potential energy curves (PECs) are generated employing ab initio calculated adiabatic and diabatic potential energy surfaces (PESs). We have implemented beyond Born-Oppenheimer (BBO) theory for constructing smooth, single-valued, and continuous diabatic PESs for five coupled electronic states [J. Phys. Chem. A 2017, 121, 6314-6326]. In the case of NO3 radical, the nonadiabatic coupling terms (NACTs) among the low-lying five electronic states, namely, X̃ 2A2 ' (12B2), A~ 2E″ (12A2 and 12B1), and B~ 2E' (12A1 and 22B2), bear the signature of Jahn-Teller (JT) interactions, pseudo JT (PJT) interactions, and accidental conical intersections (CIs). Similarly, Bz+ radical cation also exhibits JT, PJT, and accidental CIs in the interested domain of nuclear configuration space. In order to generate dressed PECs, two components of degenerate in-plane asymmetric stretching modes are selectively chosen for both the molecular species (Q 3x -Q 3y pair for NO3 radical and Q 16x -Q 16y pair for Bz+ radical cation). The JT coupling between the electronic states is essentially originated through the asymmetric stretching normal mode pair, where the coupling elements exhibit symmetric and nonlinear functional behavior along Q 3x and Q 16x normal modes.
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Affiliation(s)
- Soumya Mukherjee
- Department
of Physical Chemistry, Indian Association
for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Bijit Mukherjee
- Department
of Physical Chemistry, Indian Association
for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Joy Dutta
- Department
of Physical Chemistry, Indian Association
for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Subhankar Sardar
- Department
of Chemistry, Bhatter College, Dantan, Paschim Medinipur, 721426, India
| | - Satrajit Adhikari
- Department
of Physical Chemistry, Indian Association
for the Cultivation of Science, Jadavpur, Kolkata 700032, India
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Ramirez-Solis A, Amaro-Estrada JI, Hernández-Cobos J, Maron L. Aqueous Solvation of SmI 3: A Born-Oppenheimer Molecular Dynamics Density Functional Theory Cluster Approach. Inorg Chem 2018; 57:2843-2850. [PMID: 29424528 DOI: 10.1021/acs.inorgchem.7b03220] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We report the results of Born-Oppenheimer molecular dynamics (BOMD) simulations on the aqueous solvation of the SmI3 molecule and of the bare Sm3+ cation at room temperature using the cluster microsolvation approach including 37 and 29 water molecules, respectively. The electronic structure calculations were done using the M062X hybrid exchange-correlation functional in conjunction with the 6-31G** basis sets for oxygen and hydrogen. For the iodine and samarium atoms, the Stuttgart-Köln relativistic effective-core potentials were utilized with their associated valence basis sets. When SmI3 is embedded in the microsolvation environment, we find that substitution of the iodine ions by water molecules around Sm(III) cannot be achieved due to an insufficient number of explicit water molecules to fully solvate the four separate metal and halogen ions. Therefore, we studied the solvation dynamics of the bare Sm3+ cation with a 29-water molecule model cluster. Through the Sm-O radial distribution function and the evolution of the Sm-O distances, the present study yields a very tightly bound first rigid Sm(III) solvation shell from 2.3 to 2.9 Å whose integration leads to a coordination number of 9 water molecules and a second softer solvation sphere from 3.9 to 5 Å with 12 water molecules. No water exchange processes were found. The theoretical EXAFS spectrum is in excellent agreement with the experimental spectrum for Sm(III) in liquid water. The strong differences between the solvation patterns of Sm(III) vs Sm(II) are discussed in detail.
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Affiliation(s)
- Alejandro Ramirez-Solis
- Depto. de Física, Centro de Investigación en Ciencias-IICBA , Universidad Autónoma del Estado de Morelos , Cuernavaca , Morelos 62209 , México
| | | | | | - Laurent Maron
- Laboratoire de Physique et Chimie de Nano-objets , Université de Toulouse INSA-CNRS-UPS , 135, Avenue de Rangueil , 31077 Toulouse , France
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16
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Mukherjee S, Mukherjee B, Adhikari S. Five Electronic State Beyond Born-Oppenheimer Equations and Their Applications to Nitrate and Benzene Radical Cation. J Phys Chem A 2017; 121:6314-6326. [PMID: 28735536 DOI: 10.1021/acs.jpca.7b04592] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present explicit form of Adiabatic to Diabatic Transformation (ADT) equations and expressions of non-adiabatic coupling terms (NACTs) for a coupled five-state electronic manifold in terms of ADT angles between electronic wave functions. ADT matrices eliminate the numerical instability arising from singularity of NACTs and transform the adiabatic Schrödinger equation to its diabatic form. Two real molecular systems NO3 and C6H6+ (Bz+) are selectively chosen for the demonstration of workability of those equations. We examine the NACTs among the lowest five electronic states of the NO3 radical [X̃2A2' (12B2), Ã2E″ (12A2 and 12B1) and B̃2E' (12A1 and 22B2)], in which all types of non-adiabatic interactions, that is, Jahn-Teller (JT) interactions, Pseudo Jahn-Teller (PJT) interactions, and accidental conical intersections (CIs) are present. On the other hand, lowest five electronic states of Bz+ [X̃2E1g (12B3g and 12B2g), B̃2E2g (12Ag and 12B1g), and C̃2A2u (12B1u)] depict similar kind of complex feature of non-adiabatic effects. For NO3 radical, the two components of degenerate in-plane asymmetric stretching mode are taken as a plane of nuclear configuration space (CS), whereas in case of Bz+, two pairs are chosen: One is the pair of components of degenerate in-plane asymmetric stretching mode, and the other one is constituted with one of the components each from out-of-plane degenerate bend and in-plane degenerate asymmetric stretching modes. We calculate ab initio adiabatic potential energy surfaces (PESs) and NACTs among the lowest five electronic states at the CASSCF level using MOLPRO quantum chemistry package. Subsequently, the ADT is performed using those newly developed equations to validate the positions of the CIs, evaluate the ADT angles and construct smooth, symmetric, and continuous diabatic PESs for both the molecular systems.
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Affiliation(s)
- Soumya Mukherjee
- Department of Physical Chemistry, Indian Association for the Cultivation of Science , Jadavpur, Kolkata 700 032, India
| | - Bijit Mukherjee
- Department of Physical Chemistry, Indian Association for the Cultivation of Science , Jadavpur, Kolkata 700 032, India
| | - Satrajit Adhikari
- Department of Physical Chemistry, Indian Association for the Cultivation of Science , Jadavpur, Kolkata 700 032, India
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