Jonathan Rawlinson
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View article: Recovering Exact Vibrational Energies Within a Phase Space Electronic Structure Framework
Recovering Exact Vibrational Energies Within a Phase Space Electronic Structure Framework Open
In recent years, there has been a push to go beyond Born-Oppenheimer theory and build electronic states from a phase space perspective, i.e. parameterize electronic states by both nuclear position(R) and nuclear momentum(P). Previous empir…
View article: Symmetry Breaking as Predicted by a Phase Space Hamiltonian with a Spin Coriolis Potential
Symmetry Breaking as Predicted by a Phase Space Hamiltonian with a Spin Coriolis Potential Open
We perform electronic structure calculations for a set of molecules with degenerate spin-dependent ground states ($^3$CH$_2$, $^2$CH$_3^{\bullet}$, $^3$O$_2$) going beyond the Born-Oppenheimer approximation and accounting for nuclear motio…
View article: A Phase-Space Electronic Hamiltonian for Molecules in a Static Magnetic Field II: Quantum Chemistry Calculations with Gauge Invariant Atomic Orbitals
A Phase-Space Electronic Hamiltonian for Molecules in a Static Magnetic Field II: Quantum Chemistry Calculations with Gauge Invariant Atomic Orbitals Open
In a companion paper, we have developed a phase-space electronic structure theory of molecules in magnetic fields, whereby the electronic energy levels arise from diagonalizing a phase-space Hamiltonian $\hat H_{PS}(\bf{X},\bfΠ)$ that depe…
View article: A Phase-Space Electronic Hamiltonian for Molecules in a Static Magnetic Field I: Conservation of Total Pseudomomentum and Angular Momentum
A Phase-Space Electronic Hamiltonian for Molecules in a Static Magnetic Field I: Conservation of Total Pseudomomentum and Angular Momentum Open
We develop a phase-space electronic structure theory of molecules in magnetic fields. For a system of electrons in a magnetic field with vector potential $\bf{A}(\hat{\bf{r}})$, the usual Born-Oppenheimer Hamiltonian is the sum of the nucl…
View article: Eigenvalue crossings in equivariant families of matrices
Eigenvalue crossings in equivariant families of matrices Open
According to a result of Wigner and von Neumann [1], real symmetric matrices with a doubly degenerate lowest eigenvalue form a submanifold of codimension 2 within the space of all real symmetric matrices. This mathematical result has impor…
View article: Can The Mystery of The Born-Oppenheimer Electronic Current Density Be Explained With A Simple Phase Space Electronic Hamiltonian? Yes (And A Lot More Too)
Can The Mystery of The Born-Oppenheimer Electronic Current Density Be Explained With A Simple Phase Space Electronic Hamiltonian? Yes (And A Lot More Too) Open
We show that a phase space electronic Hamiltonian $\hat{H}_{PS}(\mathbf{X},\mathbf{P})$, parameterized by both nuclear position $\mathbf{X}$ and momentum $\mathbf{P}$, can recover not just experimental vibrational circular dichroism (VCD) …
View article: A phase-space view of vibrational energies without the Born-Oppenheimer framework
A phase-space view of vibrational energies without the Born-Oppenheimer framework Open
We show that following the standard mantra of quantum chemistry and diagonalizing the Born-Oppenheimer (BO) Hamiltonian $\hat H_{\rm BO}(\bm R)$ is not the optimal means to construct potential energy surfaces. A better approach is to diago…
View article: A Phase Space Approach to Vibrational Circular Dichroism
A Phase Space Approach to Vibrational Circular Dichroism Open
We show empirically that a phase-space non-Born-Oppenheimer electronic Hamiltonian approach to quantum chemistry (where the electronic Hamiltonian is parameterized by both nuclear position and momentum, (H(R,P)) is both a practical and acc…
View article: A simple one-electron expression for electron rotational factors
A simple one-electron expression for electron rotational factors Open
Within the context of fewest-switch surface hopping (FSSH) dynamics, one often wishes to remove the angular component of the derivative coupling between states J and K. In a previous set of papers, Shu et al. [J. Phys. Chem. Lett. 11, 1135…
View article: Practical phase-space electronic Hamiltonians for <i>ab initio</i> dynamics
Practical phase-space electronic Hamiltonians for <i>ab initio</i> dynamics Open
Modern electronic structure theory is built around the Born–Oppenheimer approximation and the construction of an electronic Hamiltonian Ĥel(X) that depends on the nuclear position X (and not the nuclear momentum P). In this article, using …
View article: Diagonalizing the Born–Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom
Diagonalizing the Born–Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom Open
This article describes a method for calculating higher order or nonadiabatic corrections in Born–Oppenheimer theory and its interaction with the translational degrees of freedom. The method uses the Wigner–Weyl correspondence to map nuclea…
View article: Total angular momentum conservation in Ehrenfest dynamics with a truncated basis of adiabatic states
Total angular momentum conservation in Ehrenfest dynamics with a truncated basis of adiabatic states Open
We show that standard Ehrenfest dynamics does not conserve linear and angular momentum when using a basis of truncated adiabatic states. However, we also show that previously proposed effective Ehrenfest equations of motion [M. Amano and K…
View article: Practical Phase-Space Electronic Hamiltonians for Ab Initio Dynamics
Practical Phase-Space Electronic Hamiltonians for Ab Initio Dynamics Open
Modern electronic structure theory is built around the Born-Oppenheimer approximation and the construction of an electronic Hamiltonian H_{el}(X) that depends on the nuclear position X (and not the nuclear momentum P). In this article, usi…
View article: A Simple One-Electron Expression for Electron Rotational Factors
A Simple One-Electron Expression for Electron Rotational Factors Open
Within the context of FSSH dynamics, one often wishes to remove the angular component of the derivative coupling between states $\left|J\right>$ and $\left|K\right>$. In a set of previous papers, Truhlar {\em et al.} posited one approach f…
View article: Diagonalizing the Born-Oppenheimer Hamiltonian via Moyal Perturbation Theory, Nonadiabatic Corrections and Translational Degrees of Freedom
Diagonalizing the Born-Oppenheimer Hamiltonian via Moyal Perturbation Theory, Nonadiabatic Corrections and Translational Degrees of Freedom Open
This article describes a method for calculating higher order or nonadiabatic corrections in Born-Oppenheimer theory and its interaction with the translational degrees of freedom. The method uses the Wigner-Weyl correspondence to map nuclea…
View article: Total Angular Momentum Conservation in Ehrenfest Dynamics with a Truncated Basis of Adiabatic States
Total Angular Momentum Conservation in Ehrenfest Dynamics with a Truncated Basis of Adiabatic States Open
We show that standard Ehrenfest dynamics does not conserve linear and angular momentum when using a basis of truncated adiabatic states. However, we also show that previously proposed effective Ehrenfest equations of motion[Amano2005,Krish…
View article: Linear and Angular Momentum Conservation in Surface Hopping Methods
Linear and Angular Momentum Conservation in Surface Hopping Methods Open
We demonstrate that, for systems with spin-orbit coupling and an odd number of electrons, the standard fewest switches surface hopping (FSSH) algorithm does not conserve the total linear or angular momentum. This lack of conservation arise…
View article: Surface Hopping, Electron Translation Factors, Electron Rotation Factors, Momentum Conservation, and Size Consistency
Surface Hopping, Electron Translation Factors, Electron Rotation Factors, Momentum Conservation, and Size Consistency Open
For a system without spin-orbit coupling, the (i) nuclear plus electronic linear momentum and (ii) nuclear plus orbital electronic angular momentum are good quantum numbers. Thus, when a molecular system undergoes a nonadiabatic transition…
View article: Capturing spin chain dynamics with periodically projected time-dependent basis
Capturing spin chain dynamics with periodically projected time-dependent basis Open
Simulating many-body quantum systems poses significant challenges due to the large size of the state space. To address this issue, we propose using an SU(2) coherent state for individual spins to simulate spins on a lattice and derive equa…
View article: Total Angular Momentum Conservation in Ab Initio Born-Oppenheimer Molecular Dynamics
Total Angular Momentum Conservation in Ab Initio Born-Oppenheimer Molecular Dynamics Open
We prove both analytically and numerically that the total angular momentum of a molecular system undergoing adiabatic Born-Oppenheimer dynamics is conserved only when pseudo-magnetic Berry forces are taken into account. This finding sheds …
View article: Representation and Conservation of Angular Momentum in the Born-Oppenheimer Theory of Polyatomic Molecules
Representation and Conservation of Angular Momentum in the Born-Oppenheimer Theory of Polyatomic Molecules Open
This paper concerns the representation of angular momentum operators in the Born-Oppenheimer theory of polyatomic molecules and the various forms of the associated conservation laws. Topics addressed include the question of whether these c…
View article: The Parallel-Transported (Quasi)-Diabatic Basis
The Parallel-Transported (Quasi)-Diabatic Basis Open
This article concerns the use of parallel transport to create a diabatic basis. The advantages of the parallel-transported basis include the facility with which Taylor series expansions can be carried out in the neighborhood of a point or …
View article: Modeling Spin-Dependent Nonadiabatic Dynamics with Electronic Degeneracy: A Phase-Space Surface-Hopping Method
Modeling Spin-Dependent Nonadiabatic Dynamics with Electronic Degeneracy: A Phase-Space Surface-Hopping Method Open
Nuclear Berry curvature effects emerge from electronic spin degeneracy and can lead to nontrivial spin-dependent (nonadiabatic) nuclear dynamics. However, such effects are not captured fully by any current mixed quantum-classical method su…
View article: A phase-space semiclassical approach for modeling nonadiabatic nuclear dynamics with electronic spin
A phase-space semiclassical approach for modeling nonadiabatic nuclear dynamics with electronic spin Open
Chemical relaxation phenomena, including photochemistry and electron transfer processes, form a vigorous area of research in which nonadiabatic dynamics plays a fundamental role. However, for electronic systems with spin degrees of freedom…
View article: The bohmion method in nonadiabatic quantum hydrodynamics
The bohmion method in nonadiabatic quantum hydrodynamics Open
Starting with the exact factorization of the molecular wavefunction, this paper presents the results from the numerical implementation in nonadiabatic molecular dynamics of the recently proposed bohmion method. Within the context of quantu…
View article: Generalised homomorphisms, measuring coalgebras and extended symmetries
Generalised homomorphisms, measuring coalgebras and extended symmetries Open
Three categories of algebras with morphisms generalising the usual set of algebra homomorphisms are described. The Sweedler product provides a hom-tensor equivalence relating these three categories, and a tool enabling the universal measur…
View article: Exactly solvable 1D model explains the low-energy vibrational level\n structure of protonated methane
Exactly solvable 1D model explains the low-energy vibrational level\n structure of protonated methane Open
A new one-dimensional model is proposed for the low-energy vibrational\nquantum dynamics of CH5+ based on the motion of an effective particle confined\nto a 60-vertex graph ${\\Gamma}_{60}$ with a single edge length parameter.\nWithin this…
View article: The simplest model to explain the vibrational level structure of protonated methane
The simplest model to explain the vibrational level structure of protonated methane Open
A new one-dimensional model is proposed for the low-energy vibrational quantum dynamics of CH5+ based on the motion of an effective particle confined to a 4-regular (quartic) 60-vertex metric graph ${\Gamma}_{60}$ with a single edge length…
View article: Exactly solvable 1D model explains the low-energy vibrational level structure of protonated methane
Exactly solvable 1D model explains the low-energy vibrational level structure of protonated methane Open
We present a simple, one-dimensional, exactly solvable model which explains not one but the first 60 vibrational eigenstates of the 6-atom molecule CH5+.
View article: The rovibrational Aharonov–Bohm effect
The rovibrational Aharonov–Bohm effect Open
The Aharonov–Bohm effect helps to explain experimentally measurable high-resolution spectra and quantum dynamics of a class of molecules.