VHEGEN: A vibronic Hamiltonian expansion generator for trigonal and tetragonal polyatomic systems

Abstract An increasing number of studies in Jahn–Teller and pseudo-Jahn–Teller effects have revealed the importance of vibronic Hamiltonians with high order expansions in vibrational coordinates. This motivates us to present VHEGEN ( V -ibronic H -amiltonian E -xpansion GEN -erator), a Python package that is capable of symbolically generating arbitrarily high order expansion formulas for the vibronic Hamiltonians. The program covers all > 6000 bimodal Jahn–Teller and pseudo-Jahn–Teller problems in trigonal and tetragonal symmetries. The generated expansions are correct, complete, and concise. VHEGEN is a useful program for future studies in Jahn–Teller and pseudo-Jahn–Teller effects. Program summary Program Title: VHEGEN Program Files doi: http://dx.doi.org/10.17632/7t5p6snkd7.1 Licensing provisions: GPLv3 Programming language: Python Nature of problem: Obtaining correct, complete, and concise high-order expansions of Jahn–Teller and pseudo-Jahn–Teller Hamiltonians in a case-by-case manner is a laborious and error-prone task. Solution method: We present a Python package to automate the utilization of our recently developed formalisms in obtaining any possible trigonal and tetragonal bimodal (pseudo-)Jahn–Teller vibronic Hamiltonian expanded to arbitrary order in vibrational coordinates.

[1]  D. Yarkony,et al.  Role of conical intersections in molecular spectroscopy and photoinduced chemical dynamics. , 2012, Annual review of physical chemistry.

[2]  Robert P. Krawczyk,et al.  Theoretical investigation of Jahn-Teller and pseudo-Jahn-Teller interactions in the ammonia cation , 2003 .

[3]  Wolfgang Eisfeld,et al.  Full-dimensional diabatic potential energy surfaces including dissociation: the ²E″ state of NO₃. , 2014, The Journal of chemical physics.

[4]  A. Viel,et al.  Higher order (A+E)⊗e pseudo-Jahn-Teller coupling , 2005 .

[5]  T. Barckholtz.  Quantitative insights about molecules exhibiting Jahn-Teller and related effects , 1998 .

[6]  Tao Zeng,et al.  Revisiting the (E + A) ⊗ (e + a) problems of polyatomic systems with trigonal symmetry: general expansions of their vibronic Hamiltonians. , 2017, Physical chemistry chemical physics : PCCP.

[7]  B. Applegate,et al.  Explorations of conical intersections and their ramifications for chemistry through the Jahn-Teller effect. , 2003, Chemical Society reviews.

[8]  Riley J. Hickman,et al.  General formalism for vibronic Hamiltonians in tetragonal symmetry and beyond. , 2018, Physical chemistry chemical physics : PCCP.

[9]  J. Stanton,et al.  Jet cooled cavity ringdown spectroscopy of the Ã(2)E(″)←X˜(2)A2 (') transition of the NO3 radical. , 2015, The Journal of chemical physics.

[10]  Basile F. E. Curchod,et al.  Ab Initio Nonadiabatic Quantum Molecular Dynamics. , 2018, Chemical reviews.

[11]  W. Domcke,et al.  High-order expansion of T2×e Jahn–Teller potential-energy surfaces in tetrahedral systems , 2010 .

[12]  L. Cederbaum,et al.  Approximately diabatic states from block diagonalization of the electronic Hamiltonian , 1988 .

[13]  W. Domcke,et al.  Jahn-Teller and spin-orbit coupling effects in transition-metal trifluorides , 2011 .

[14]  W. Domcke,et al.  High-order expansion of T(2)xt(2) Jahn-Teller potential-energy surfaces in tetrahedral molecules. , 2010, The Journal of chemical physics.

[15]  I. Bersuker,et al.  Modern aspects of the Jahn-Teller effect theory and applications to molecular problems. , 2001, Chemical reviews.

[16]  W. Scott,et al.  Group Theory. , 1964 .

[17]  Tao Zeng,et al.  Hamiltonian formalism of spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in trigonal and tetragonal symmetries. , 2019, Physical chemistry chemical physics : PCCP.

[18]  P. Botschwina,et al.  Theoretical study of the Jahn–Teller effect in X̃ 2E CH3O , 2000 .

[19]  Isaac B. Bersuker,et al.  Vibronic interactions in molecules and crystals , 1989 .

[20]  S. Mahapatra,et al.  Exploring the Jahn-Teller and pseudo-Jahn-Teller conical intersections in the ethane radical cation. , 2005, The Journal of chemical physics.

[21]  Riley J. Hickman,et al.  General Formalism of Vibronic Hamiltonians for Tetrahedral and Octahedral Systems: Problems That Involve T, E States and t, e Vibrations. , 2017, Journal of chemical theory and computation.

[22]  Tao Zeng.  A diabatization protocol that includes spin-orbit coupling. , 2017, The Journal of chemical physics.

[23]  Travis E. Oliphant,et al.  Guide to NumPy , 2015 .

[24]  W. Eisfeld,et al.  Towards a higher-order description of Jahn-Teller coupling effects in molecular spectroscopy: The (A)over-tilde(2)E '' state of NO3 , 2008 .

[25]  Swarnendu Bhattacharyya,et al.  Quantum dynamics on a three-sheeted six-dimensional ab initio potential-energy surface of the phosphine cation: Simulation of the photoelectron spectrum and the ultrafast radiationless decay dynamics. , 2015, The Journal of chemical physics.

[26]  W. Domcke,et al.  Ab initio study of dynamical E × e Jahn-Teller and spin-orbit coupling effects in the transition-metal trifluorides TiF3, CrF3, and NiF3. , 2012, The Journal of chemical physics.

[27]  J. Stanton,et al.  A simple quasi-diabatization scheme suitable for spectroscopic problems based on one-electron properties of interacting states. , 2016, The Journal of chemical physics.

[28]  Swarnendu Bhattacharyya,et al.  The (E + A) × (e + a) Jahn-Teller and pseudo-Jahn-Teller Hamiltonian including spin-orbit coupling for trigonal systems. , 2014, The journal of physical chemistry. A.

[29]  S. Mahapatra,et al.  Construction scheme for regularized diabatic states , 2001 .

[30]  M. Halcrow,et al.  Jahn-Teller distortions in transition metal compounds, and their importance in functional molecular and inorganic materials. , 2013, Chemical Society reviews.

[31]  H. Weyl.  The Classical Groups , 1940 .

[32]  K. Kawaguchi,et al.  Vibronic interactions in the NO3 radical , 1991 .

[33]  L. Cederbaum,et al.  Multimode Jahn–Teller and pseudo‐Jahn–Teller effects in BF+3 , 1983 .

[34]  Juan-Qin Li,et al.  The Jahn-Teller effect in CH3Cl+(X̃2E): a combined high-resolution experimental measurement and ab initio theoretical study. , 2012, The Journal of chemical physics.

[35]  Xue‐Bin Wang,et al.  Vibronic interaction in CO3- photo-detachment: Jahn-Teller effects beyond structural distortion and general formalisms for vibronic Hamiltonians in trigonal symmetries. , 2019, Physical chemistry chemical physics : PCCP.

[36]  T. Mondal.  On the higher-order T2 ⊗ (e + t2) Jahn-Teller coupling effects in the photodetachment spectrum of the alanate anion (AlH4-). , 2018, Physical chemistry chemical physics : PCCP.

[37]  D. Yarkony,et al.  Nonadiabatic quantum chemistry--past, present, and future. , 2012, Chemical reviews.

[38]  U. Manthe,et al.  Photoionization-induced dynamics of ammonia: ab initio potential energy surfaces and time-dependent wave packet calculations for the ammonia cation. , 2006, The Journal of chemical physics.

[39]  A. Viel,et al.  Effects of higher order Jahn-Teller coupling on the nuclear dynamics. , 2004, The Journal of chemical physics.

[40]  Don W. Arnold,et al.  Examination of the 2A’2 and 2E‘ states of NO3 by ultraviolet photoelectron spectroscopy of NO−3 , 1991 .

[41]  F. Merkt,et al.  Rotationally resolved photoelectron spectroscopic study of the Jahn-Teller effect in allene. , 2009, The Journal of chemical physics.

[42]  S. Mahapatra,et al.  Multimode Jahn–Teller and pseudo-Jahn–Teller coupling effects in the photoelectron spectrum of CH3F , 2004 .

[43]  Henry K Tran,et al.  Quantifying the effects of higher order coupling terms on fits using a second order Jahn-Teller Hamiltonian , 2018 .

[44]  G. Worth,et al.  Allene and pentatetraene cations as models for intramolecular charge transfer: vibronic coupling Hamiltonian and conical intersections. , 2005, The Journal of chemical physics.

[45]  Isaac B. Bersuker,et al.  The Jahn-Teller Effect , 2006 .

[46]  M. Born,et al.  Dynamical Theory of Crystal Lattices , 1954 .

[47]  I. Bersuker.  Pseudo-Jahn-teller effect--a two-state paradigm in formation, deformation, and transformation of molecular systems and solids. , 2013, Chemical reviews.