Hamiltonian formalism of spin–orbit Jahn–Teller and pseudo-Jahn–Teller problems in trigonal and tetragonal symmetries

Wang, Kun; Zeng, Tao

doi:10.1039/c9cp03584b

“…So far, we have successfully derived arbitrarily high order expansion formulas for all bimodal JT/pJT problems in trigonal symmetries, 43,44 tetragonal symmetries, 45 cubic group symmetries, 46,47 and spin-orbit JT/pJT problems in trigonal and tetragonal symmetries. 48 These formalisms are inclusive, yet not enough. Problems with more than two sets of JT/pJT active vibrational modes and of higher axial symmetries, e.g., pentagonal (cyclopentadienyl ring 49,50 ), hexagonal (benzene 51,52 ), and in general n-gonal (nanotubes, nanohoops, and nanoloops of different sizes [53][54][55][56] ), await to be addressed.…”

Section: Introductionmentioning

confidence: 99%

“…These pioneering studies motivated us to derive JT/pJT expansion formulas that are of arbitrarily high orders and are as inclusive as for one class of symmetries, instead of one symmetry. So far, we have successfully derived arbitrarily high order expansion formulas for all bimodal JT/pJT problems in trigonal symmetries, , tetragonal symmetries, cubic group symmetries, , and spin–orbit JT/pJT problems in trigonal and tetragonal symmetries . These formalisms are inclusive, yet not enough.…”

Section: Introductionmentioning

confidence: 99%

Unified Hamiltonian Formalism of Jahn–Teller and Pseudo-Jahn–Teller Problems in Axial Symmetries

Brown

¹

,

Lang

²

,

Zeng

³

2021

J. Chem. Theory Comput.

Self Cite

View full text Add to dashboard Cite

A formalism for expansions of all Jahn-Teller and pseudo-Jahn-Teller Hamiltonian operators in all axial symmetries is presented. The formalism provides Hamiltonian expansions up to arbitrarily high order and including an arbitrary number of vibra?tional modes, which are of arbitrary types. It consists of three equations and two tables. The formalism is user-friendly since it can be used without understanding its derivation. An example of E00 3 ⊗ e 0 1 Jahn-Teller interaction of cycloheptatrienyl cation is used to demonstrate the correctness of the formalism. A Python program is devel?oped to automate the generation of Hamiltonian expansions for all axial Jahn-Teller and pseodo-Jahn-Teller problems, , and interface the expansions to quantum dynamics simulation program. This is the first unified Hamiltonian formalism for axial Jahn?Teller and pseudo-Jahn-Teller problems. And it is the only one. File list (2) download file view on ChemRxiv paper.pdf (3.24 MiB) download file view on ChemRxiv SI.pdf (491.06 KiB)

show abstract

“…So far, we have successfully derived arbitrarily high order expansion formulas for all bimodal JT/pJT problems in trigonal symmetries, 43,44 tetragonal symmetries, 45 cubic group symmetries, 46,47 and spin-orbit JT/pJT problems in trigonal and tetragonal symmetries. 48 These formalisms are inclusive, yet not enough. Problems with more than two sets of JT/pJT active vibrational modes and of higher axial symmetries, e.g., pentagonal (cyclopentadienyl ring 49,50 ), hexagonal (benzene 51,52 ), and in general n-gonal (nanotubes, nanohoops, and nanoloops of different sizes [53][54][55][56] ), await to be addressed.…”

Section: Introductionmentioning

confidence: 99%

A Unified Hamiltonian Formalism of Jahn-Teller and Pseudo-Jahn-Teller Problems in Axial Symmetries

Brown¹,

Lang²,

Zeng

³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

A formalism for expansions of all Jahn-Teller and pseudo-Jahn-Teller Hamiltonian operators in all axial symmetries is presented. The formalism provides Hamiltonian expansions up to arbitrarily high order and including an arbitrary number of vibra?tional modes, which are of arbitrary types. It consists of three equations and two tables. The formalism is user-friendly since it can be used without understanding its derivation. An example of E00 3 ⊗ e 0 1 Jahn-Teller interaction of cycloheptatrienyl cation is used to demonstrate the correctness of the formalism. A Python program is devel?oped to automate the generation of Hamiltonian expansions for all axial Jahn-Teller and pseodo-Jahn-Teller problems, , and interface the expansions to quantum dynamics simulation program. This is the first unified Hamiltonian formalism for axial Jahn?Teller and pseudo-Jahn-Teller problems. And it is the only one.

show abstract

“…So far, we have successfully derived arbitrarily high order expansion formulas for all bimodal JT/pJT problems in trigonal symmetries, 43,44 tetragonal symmetries, 45 cubic group symmetries, 46,47 and spin-orbit JT/pJT problems in trigonal and tetragonal symmetries. 48 These formalisms are inclusive, yet not enough. Problems with more than two sets of JT/pJT active vibrational modes and of higher axial symmetries, e.g., pentagonal (cyclopentadienyl ring 49,50 ), hexagonal (benzene 51,52 ), and in general n-gonal (nanotubes, nanohoops, and nanoloops of different sizes [53][54][55][56] ), await to be addressed.…”

Section: Introductionmentioning

confidence: 99%

A Unified Hamiltonian Formalism of Jahn-Teller and Pseudo-Jahn-Teller Problems in Axial Symmetries

Brown¹,

Lang²,

Zeng³

2021

Preprint

Self Cite

0

View full text Add to dashboard Cite

A formalism for expansions of all Jahn-Teller and pseudo-Jahn-Teller Hamiltonian operators in all axial symmetries is presented. The formalism provides Hamiltonian expansions up to arbitrarily high order and including an arbitrary number of vibra?tional modes, which are of arbitrary types. It consists of three equations and two tables. The formalism is user-friendly since it can be used without understanding its derivation. An example of E00 3 ⊗ e 0 1 Jahn-Teller interaction of cycloheptatrienyl cation is used to demonstrate the correctness of the formalism. A Python program is devel?oped to automate the generation of Hamiltonian expansions for all axial Jahn-Teller and pseodo-Jahn-Teller problems, , and interface the expansions to quantum dynamics simulation program. This is the first unified Hamiltonian formalism for axial Jahn?Teller and pseudo-Jahn-Teller problems. And it is the only one.

show abstract

Hamiltonian formalism of spin–orbit Jahn–Teller and pseudo-Jahn–Teller problems in trigonal and tetragonal symmetries

Abstract: A formalism for expansions of all bimodal spin–orbit Jahn–Teller and pseudo-Jahn–Teller Hamiltonian operators in trigonal and tetragonal symmetries is presented.

Cited by 12 publications

References 72 publications

Unified Hamiltonian Formalism of Jahn–Teller and Pseudo-Jahn–Teller Problems in Axial Symmetries

Unified Hamiltonian Formalism of Jahn–Teller and Pseudo-Jahn–Teller Problems in Axial Symmetries

A Unified Hamiltonian Formalism of Jahn-Teller and Pseudo-Jahn-Teller Problems in Axial Symmetries

A Unified Hamiltonian Formalism of Jahn-Teller and Pseudo-Jahn-Teller Problems in Axial Symmetries

Contact Info

Product

Resources

About