Diagrammatic theories for the vibrational many-body problem

Faucheaux, Jacob A.

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https://hdl.handle.net/2142/99490 Copy

Description

Title

Diagrammatic theories for the vibrational many-body problem

Author(s)

Faucheaux, Jacob A.

Issue Date

2017-11-28

Director of Research (if dissertation) or Advisor (if thesis)

Hirata, So

Doctoral Committee Chair(s)

Hirata, So

Committee Member(s)

• Gruebele, Martin
• Makri, Nancy
• Wagner, Lucas

Department of Study

Chemistry

Discipline

Chemistry

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Coupled-cluster
• Vibrational structure
• Anharmonic
• Diagrams

Abstract

Anharmonic vibrational many-body methods are developed for and applied to small molecules and extended systems in a bound potential energy surface (PES). Diagrammatically size-consistent and basis-set-free vibrational coupled-cluster (XVCC) theory for both zero-point energies and transition frequencies, the latter through the equation-of-motion (EOM) formalism, is defined for an $n$th-order Taylor-series PES. Quantum-field-theoretical tools (the rules of normal-ordered second quantization and Feynman--Goldstone diagrams) for deriving their working equations are established. The equations of XVCC and EOM-XVCC are derived and implemented with the aid of computer algebra. Algorithm optimizations known as strength reduction, intermediate reuse, and factorization are carried out before code generation,producing algorithms with optimal cost scaling. A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. An extended STEOM-XVCC (Ext-STEOM-XVCC) method is defined as an $m$th order configuration interaction method with the doubly similarity-transformed Hamiltonian including up to $m$th-order excitation operators. Because the doubly transformed Hamiltonian is dressed with higher-order anharmonic effects, the frequencies of overtones and combinations obtained are different and superior to the corresponding EOM-XVCC method. We compare and contrast the Ext-STEOM-XVCC method to its electronic counterpart. We apply the previously established second-order size-extensive vibrational many-body perturbation (XVMP2) method to the anharmonic phonon dispersion curves of a model two-mass system and the optical phonons of polyethylene. We obtain accurate results despite the presence of multiple Fermi-resonances in the crystalline systems.

Graduation Semester

2017-12

Type of Resource

text

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http://hdl.handle.net/2142/99490

Copyright and License Information

Copyright 2017 Jacob Faucheaux

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