Time-dependent Coupled-cluster Research Articles

Time‐dependent coupled‐cluster theory

AbstractRecent years have witnessed an increasing interest in time‐dependent coupled‐cluster (TDCC) theory for simulating laser‐driven electronic dynamics in atoms and molecules, and for simulating molecular vibrational dynamics. Starting from the time‐dependent bivariational principle, we review different flavors of single‐reference TDCC theory with either orthonormal static, orthonormal time‐dependent, or biorthonormal time‐dependent spin orbitals. The time‐dependent extension of equation‐of‐motion coupled‐cluster theory is also discussed, along with the applications of TDCC methods to the calculation of linear absorption spectra, linear and low‐order nonlinear response functions, highly nonlinear high harmonic generation spectra and ionization dynamics. In addition, the role of TDCC theory in finite‐temperature many‐body quantum mechanics is briefly described along with a few other application areas.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Theoretical and Physical Chemistry > Spectroscopy Software > Simulation Methods

Interpretation of Coupled-Cluster Many-Electron Dynamics in Terms of Stationary States.

We demonstrate theoretically and numerically that laser-driven many-electron dynamics, as described by bivariational time-dependent coupled-cluster (CC) theory, may be analyzed in terms of stationary-state populations. Projectors heuristically defined from linear response theory and equation-of-motion CC theory are proposed for the calculation of stationary-state populations during interaction with laser pulses or other external forces, and conservation laws of the populations are discussed. Numerical tests of the proposed projectors, involving both linear and nonlinear optical processes for He and Be atoms and for LiH, CH+, and LiF molecules show that the laser-driven evolution of the stationary-state populations at the coupled-cluster singles-and-doubles (CCSD) level is very close to that obtained by full configuration interaction (FCI) theory, provided that all stationary states actively participating in the dynamics are sufficiently well approximated. When double-excited states are important for the dynamics, the quality of the CCSD results deteriorates. Observing that populations computed from the linear response projector may show spurious small-amplitude, high-frequency oscillations, the equation-of-motion projector emerges as the most promising approach to stationary-state populations.

Equation of motion coupled-cluster for core excitation spectra: Two complementary approaches.

This paper presents core excitation spectra from coupled-cluster (CC) theory obtained from both a time-independent and a new time-dependent formalism. The conventional time-independent CC formulation for excited states is the equation-of-motion (EOM-CC) method whose eigenvalues and eigenvectors describe the core excited states. An alternative computational procedure is offered by a time-dependent CC description. In that case, the dipole transition operator is expressed in the CC effective Hamiltonian form and propagated with respect to time. The absorption spectrum is obtained from the CC dipole autocorrelation function via a Fourier transformation. Comparisons are made among the time-dependent results obtained from second-order perturbation theory, to coupled cluster doubles and their linearized forms (CCD and LCCD), to CC singles and doubles (CCSD) and the linearized form (LCCSD). In the time-independent case, considerations of triples (EOM-CCSDT) and quadruples (EOM-CCSDTQ) are used to approach sub-electron volt accuracy. A particular target is the allyl radical, as an example of an open-shell molecule. As the results have to ultimately be the same, the two procedures offer a complementary approach toward analyzing experimental results.

Linear Absorption Spectra from Explicitly Time-Dependent Equation-of-Motion Coupled-Cluster Theory.

We report an explicitly time-dependent approach to the generation of linear absorption spectra for molecular systems within the framework of equation-of-motion (EOM) coupled-cluster (CC) theory. While most time-dependent CC approaches consider the perturbation and time-evolution of a CC wave function, the present work considers the time-evolution of a CC dipole function. The dipole function formalism introduces no approximations and requires the evolution of only one time-dependent quantity, either the left or right dipole function. This time-dependent framework can be used to compute linear absorption spectra for molecules with a high density of states over a broad spectral range, a case for which conventional frequency-domain computations may become impractical. We validate the approach by comparing absorption spectra for small molecules computed at EOM second-order approximate CC (CC2) and time-dependent EOM-CC2 (TD-EOM-CC2) levels of theory. TD-EOM-CC2 computations are also used to predict extreme ultraviolet absorption spectra for third-row ions that are in reasonable agreement with experiment.

Ab initio quantum dynamics using coupled-cluster

The curse of dimensionality (COD) limits the current state-of-the-art ab initio propagation methods for non-relativistic quantum mechanics to relatively few particles. For stationary structure calculations, the coupled-cluster (CC) method overcomes the COD in the sense that the method scales polynomially with the number of particles while still being size-consistent and extensive. We generalize the CC method to the time domain while allowing the single-particle functions to vary in an adaptive fashion as well, thereby creating a highly flexible, polynomially scaling approximation to the time-dependent Schrödinger equation. The method inherits size-consistency and extensivity from the CC method. The method is dubbed orbital-adaptive time-dependent coupled-cluster, and is a hierarchy of approximations to the now standard multi-configurational time-dependent Hartree method for fermions. A numerical experiment is also given.

Time Dependent Coupled Cluster Approach to Resonance Raman Excitation Profiles from General Anharmonic Surfaces

A time dependent coupled cluster approach to the calculation of Resonance Raman excitation profiles on general anharmonic surfaces is presented. The vibrational wave functions on the ground electronic surface are obtained by the coupled cluster method (CCM). It is shown that the propagation of the vibrational ground state on the upper surface is equivalent to propagation of the vacuum state by an effective hamiltonian generated by the similarity transformation of the vibrational hamiltonian of that surface by the CCM wave operator of the lower surface up to a normalization constant. This time propagation is carried out by the time-dependent coupled cluster method in a time dependent frame. Numerical studies are presented to asses the validity of the approach.

Size-consistent approach and density analysis of hyperpolarizability: Second hyperpolarizabilities of polymeric systems with and without defects

Various size-consistent approaches to the calculation of molecular hyperpolarizabilities are analyzed based on the double perturbation theory. General equations for the nth-order response property with respect to an external time-independent field are derived on the basis of the Rayleigh–Schrödinger perturbation theory (RSPT) and the coupled-cluster (CC) theory. The corresponding equations for the time-dependent case are also derived by the CC formalism, which is referred to as the time-dependent CC (TDCC) method. In order to clarify the spatial characteristics of polarizability and hyperpolarizability, we present an analysis method using a new concept ‘‘the polarizability and hyperpolarizability densities.’’ As an application of the size-consistent methods, the static second hyperpolarizabilities (γ) of π-conjugated polymeric systems are calculated by the use of the uncoupled (UCHF), and coupled-Hartree–Fock (CHF) methods combined with the semiempirical INDO approximation. Characteristics of γ values calculated for regular polyenes, solitonlike polyenes and donor(D)–acceptor(A) disubstituted polyenes are investigated, particularly in relation to the chain-length effect. Further, we employ γ density analysis method, in which the third derivatives of the Mulliken charge densities against applied electric fields are plotted for exploring the local contributions of the constituent atoms to γ values. Results for the finite polyenes are also extrapolated to an infinity of the chain length to predict the intrinsic γ values per unit carbon–carbon (CC) bond of polymeric chains. Furthermore, the CHF+Mo/ller–Plesset second-order perturbation (MP2) method in the PPP approximation is applied to polymeric systems with larger chain length in order to elucidate the electron correlation effects on the chain-length dependencies of γ values.

A multireference coupled-cluster approach to quantum dynamics

A time-dependent coupled-cluster(TDCC) formalism with a multireference model space for studying quantum dynamics is presented. The evolution operator U acting on the model space is factorized as U ex U M where U M evolves in the model space and U ex brings in virtual functions. Both U ex and U M are written as normal ordered exponentials involving cluster operators. The evolution of U M is governed by an effective Hamiltonian that is size-extensive. An illustrative application on a nontrivial problem indicates the potentiality of the formalism.