Second Linear Response Theory and the Analytic Calculation of Excited-State Properties

Mosquera, Martín A.; Jones, Leighton O.; Kang, Gyeongwon; Ratner, Mark A.; Schatz, George C.

doi:10.1021/acs.jpca.0c10152

Cited by 5 publications

(5 citation statements)

References 30 publications

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“…We showed the formalism to be consistent with linear and quadratic CC response theories, and validated it successfully with model systems [50]. SR theory is an extension of previous work focused on the linear response of excited states [51][52][53]. In this work, we show further developments of SR theory in which, by using three TD excitation vectors, the expectation value of a quantum observable as a function of time can be predicted, and this includes probabilities and coherences.…”

Section: Introductionsupporting

confidence: 56%

Excited-state response theory within the context of the coupled-cluster formalism

Mosquera

2022

Phys. Rev. A

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The propagation of general electronic quantum states provides information of the interaction of molecular systems with external driving fields. These can also offer understandings regarding non-adiabatic quantum phenomena. Well established methods focus mainly on propagating a quantum system that is initially described exclusively by the ground state wavefunction. In this work, we expand a previously developed formalism within coupled cluster theory, called second response theory, so it propagates quantum systems that are initially described by a general linear combination of different states, which can include the ground state, and show how with a special set of time-dependent cluster operators such propagations are performed. Our theory shows strong consistency with numerically exact results for the determination of quantum mechanical observables, probabilities, and coherences. We discuss unperturbed non-stationary states within second response theory and their ability to predict matrix elements that agree with those found in linear and quadratic response theories. This work also discusses an approximate regularized methodology to treat systems with potential instabilities in their ground-state cluster amplitudes, and compare such approximations with respect to reference results from standard unitary theory.

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Section: Introductionsupporting

confidence: 56%

Excited-state response theory within the context of the coupled-cluster formalism

Mosquera

2022

Phys. Rev. A

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“…Hτ,µ (t)e +x(t;0) + λl (t)e −x(t;0) [ Hτ,µ (t), xr (t)]e +x(t;0) 0 (68) in which λl,r (t = 0) = J Y J ΛJ (69) and…”

Section: B Propagation From An Arbitrary Initial Statementioning

confidence: 99%

“…These are quantities such as matrix elements to study transitions between excited states, as well as permanent dipoles of such states. This formulation is based on an alternative linear response theory we developed previously, dubbed second linear response theory (SLR) [67][68][69]. We have applied it before within the context of time-dependent (TD) density functional theory to organic semiconductors.…”

Section: Introductionmentioning

confidence: 99%

Excited-State Response Theory Within the Context of the Coupled-Cluster Formalism

Mosquera¹

2022

Preprint

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Time-dependent response theories are foundational to the development of algorithms that determine quantum properties of electronic excited states of molecules and periodic systems. They are employed in wave-function, density-functional, and semiempirical methods, and are applied in an incremental order: linear, quadratic, cubic, etc. Linear response theory is known to produce electronic transitions from ground to excited state, and vice versa. In this work, a linear-response approach, within the context of the coupled cluster formalism, is developed to offer transition elements between different excited states (including permanent elements), and related properties.Our formalism, second linear response theory, is consistent with quadratic response theory, and can serve as an alternative to develop and study excited-state theoretical methods, including pathways for algorithmic acceleration. This work also formulates an extension of our theory for general propagations under non-linear external perturbations, where the observables are given by linked expressions which can predict their time-evolution under arbitrary initial states and could serve as a means of constructing general state propagators. A connection with the physics of wavefunction theory is developed as well, in which dynamical cluster operator amplitudes are related to wavefunction linear superposition coefficients.

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“…In this subsection, we follow similar steps formulated in refs and but adapted for the present theory. We expand the Hamiltonian as The perturbed Hxc (Hartree exchange–correlation) contribution is where f Hxc ( r , r ′) is the Hxc kernel.…”

Section: Theorymentioning

confidence: 99%

Density Functional Calculations Based on the Exponential Ansatz

Mosquera

2021

J. Phys. Chem. A

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This work explores the application of the singles-based exponential ansatz to density functional calculations. In contrast to the standard approach where Kohn–Sham (KS) orbitals are determined prior to computing molecular quantities of interest, we consider the single-reference Hartree–Fock wave function as a starting point. Applying the exponential ansatz to this single reference gives an auxiliary wave function that is employed to calculate the electronic properties of the system. This wave function is determined self-consistently through the standard KS Hamiltonian but evaluated over the Hartree–Fock molecular orbital basis. By using spin-symmetry breaking, we recover size-consistent results free of unphysical fractional charges in the dissociation limit. Our method shows consistency with standard KS density functional calculations when the system geometry is similar to the equilibrium one or in repulsive configurations. For moderately long distances between atoms, not at dissociation, because of self-interaction the exponential ansatz may give instabilities in the form of large cluster amplitudes. To avoid these, this work introduces a relatively simple regularization method that preserves size-consistency and penalizes high amplitudes of the cluster operator, whereas the results remain physically meaningful. We also present the time-dependent extension of our theory and show that it can feature quantum states where multiple electrons are excited.

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Second Linear Response Theory and the Analytic Calculation of Excited-State Properties

Cited by 5 publications

References 30 publications

Excited-state response theory within the context of the coupled-cluster formalism

Excited-state response theory within the context of the coupled-cluster formalism

Excited-State Response Theory Within the Context of the Coupled-Cluster Formalism

Density Functional Calculations Based on the Exponential Ansatz

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