arXiv subjects

David A. Mazziotti

Publications and source records attributed to David A. Mazziotti.

89 records · Page 5Linked to original sources

arXiv2018

Quantum signature of exciton condensation

Exciton condensation, a Bose-Einstein-like condensation of excitons, was recently reported in an electronic double layer (EDL) of graphene. We show that a universal quantum signature for exciton condensation can be used to both identity and quantify exciton condensation in molecular systems from direct calculations of the two-electron reduced density matrix. Computed large eigenvalues in the particle-hole reduced-density matrices of pentacene and hexacene EDLs reveal the beginnings of condensation, suggesting the potential for exciton condensation in smaller scale molecular EDLs.

physics.chem-ph↗

arXiv2018

Strong Electron Correlation in Nitrogenase Cofactor, FeMoco

FeMoco, MoFe$_7$S$_9$C, has been shown to be the active catalytic site for the reduction of nitrogen to ammonia in the nitrogenase protein. An understanding of its electronic structure including strong electron correlation is key to designing mimic catalysts capable of ambient nitrogen fixation. Active spaces ranging from [54, 54] to [65, 57] have been predicted for a quantitative description of FeMoco's electronic structure. However, a wavefunction approach for a singlet state using a [54,54] active space would require 10$^{29}$ variables. In this work, we systematically explore the active-space size necessary to qualitatively capture strong correlation in FeMoco and two related moieties, MoFe$_3$S$_7$ and Fe$_4$S$_7$. Using CASSCF and 2-RDM methods, we consider active-space sizes up to [14,14] and [30,30], respectively, with STO-3G, 3-21G, and DZP basis sets and use fractional natural-orbital occupation numbers to assess the level of multireference electron correlation, an examination of which reveals a competition between single-reference and multi-reference solutions to the electronic Schrödinger equation for smaller active spaces and a consistent multi-reference solution for larger active spaces.

physics.chem-ph↗

arXiv2016

Necessary N-representability Constraints from Time-reversal Symmetry for Periodic Systems

The variational calculation of the two-electron reduced density matrix (2-RDM) is extended to periodic molecular systems. If the 2-RDM theory is extended to the periodic case without consideration of time-reversal symmetry, however, it can yields energies that are significantly lower than the correct energies. We derive and implement linear constraints that enforce time-reversal symmetry on the 2-RDM without destroying its computationally favorable block-diagonal structure from translational invariance. Time-reversal symmetry is distinct from space-group or spin (SU(2)) symmetries which can be expressed by unitary transformations. The time-reversal symmetry constraints are demonstrated through calculations of the metallic hydrogen chain and the one-dimensional lithium hydride crystal.

physics.chem-ph↗

arXiv2016

Accurate Non-adiabatic Quantum Dynamics from Pseudospectral Sampling of Time-dependent Gaussian Basis Sets

Quantum molecular dynamics requires an accurate representation of the molecular potential energy surface from a minimal number of electronic structure calculations, particularly for nonadiabatic dynamics where excited states are required. In this paper, we employ pseudospectral sampling of time-dependent Gaussian basis functions for the simulation of non-adiabatic dynamics. Unlike other methods, the pseudospectral Gaussian molecular dynamics tests the Schrödinger equation with $N$ Dirac delta functions located at the centers of the Gaussian functions reducing the scaling of potential energy evaluations from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$. By projecting the Gaussian basis onto discrete points in space, the method is capable of efficiently and quantitatively describing nonadiabatic population transfer and intra-surface quantum coherence. We investigate three model systems; the photodissociation of three coupled Morse oscillators, the bound state dynamics of two coupled Morse oscillators, and a two-dimensional model for collinear triatomic vibrational dynamics. In all cases, the pseudospectral Gaussian method is in quantitative agreement with numerically exact calculations. The results are promising for nonadiabatic molecular dynamics in molecular systems where strongly correlated ground or excited states require expensive electronic structure calculations.

physics.chem-ph↗

arXiv2014

Comparison of one-dimensional and quasi-one-dimensional Hubbard models from the variational two-electron reduced-density-matrix method

Minimizing the energy of an $N$-electron system as a functional of a two-electron reduced density matrix (2-RDM), constrained by necessary $N$-representability conditions (conditions for the 2-RDM to represent an ensemble $N$-electron quantum system), yields a rigorous lower bound to the ground-state energy in contrast to variational wavefunction methods. We characterize the performance of two sets of approximate constraints, (2,2)-positivity (DQG) and approximate (2,3)-positivity (DQGT) conditions, at capturing correlation in one-dimensional and quasi-one-dimensional (ladder) Hubbard models. We find that, while both the DQG and DQGT conditions capture both the weak and strong correlation limits, the more stringent DQGT conditions improve the ground-state energies, the natural occupation numbers, the pair correlation function, the effective hopping, and the connected (cumulant) part of the 2-RDM. We observe that the DQGT conditions are effective at capturing strong electron correlation effects in both one- and quasi-one-dimensional lattices for both half filling and less-than-half filling.

physics.chem-ph↗

arXiv2014

Global solutions of restricted open-shell Hartree-Fock theory from semidefinite programming with applications to strongly correlated quantum systems

We present a density matrix approach for computing global solutions of restricted open-shell Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. While wave function approaches to Hartree-Fock theory yield an upper bound to the Hartree-Fock energy, we derive a semidefinite relaxation of Hartree-Fock theory that yields a rigorous lower bound on the Hartree-Fock energy. We also develop an upper-bound algorithm in which Hartree-Fock theory is cast as a SDP with a nonconvex constraint on the rank of the matrix variable. Equality of the upper- and lower-bound energies guarantees that the computed solution is the globally optimal solution of Hartree-Fock theory. The work extends a previously presented method for closed-shell systems [S. Veeraraghavan and D. A. Mazziotti, Phys. Rev. A89, 010502R (2014)]. For strongly correlated systems the SDP approach provides an alternative to the locally optimized Hartree-Fock energies and densities with a certificate of global optimality. Applications are made to the potential energy curves of C2, CN, Cr2, and NO2.

physics.chem-ph↗

arXiv2014

Generalized Pauli conditions on the spectra of one-electron reduced density matrices of atoms and molecules

The Pauli exclusion principle requires the spectrum of the occupation numbers of the one-electron reduced density matrix (1-RDM) to be bounded by one and zero. However, for a 1-RDM from a wave function, there exist additional conditions on the spectrum of occupation numbers, known as pure N-representability conditions or generalized Pauli conditions. For atoms and molecules, we measure through a Euclidean-distance metric the proximity of the 1-RDM spectrum to the facets of the convex set (polytope) generated by the generalized Pauli conditions. For the ground state of any spin symmetry, as long as time-reversal symmetry is considered in the definition of the polytope, we find that the 1-RDM's spectrum is pinned to the boundary of the polytope. In contrast, for excited states, we find that the 1-RDM spectrum is not pinned. Proximity of the 1-RDM to the boundary of the polytope provides a measurement and classification of electron correlation and entanglement within the quantum system. For comparison, this distance to the boundary of the generalized Pauli conditions is also compared to the distance to the polytope of the traditional Pauli conditions, and the distance to the nearest 1-RDM spectrum from a Slater determinant. We explain the difference in pinning in the ground- and excited-state 1-RDMs through a connection to the N-representability conditions of the two-electron reduced density matrix.

physics.chem-ph↗

arXiv2014

Molecule-optimized Basis Sets and Hamiltonians for Accelerated Electronic Structure Calculations of Atoms and Molecules

Molecule-optimized basis sets, based on approximate natural orbitals, are developed for accelerating the convergence of quantum calculations with strongly correlated (multi-referenced) electrons. We use a low-cost approximate solution of the anti-Hermitian contracted Schr{ö}dinger equation (ACSE) for the one- and two-electron reduced density matrices (RDMs) to generate an approximate set of natural orbitals for strongly correlated quantum systems. The natural-orbital basis set is truncated to generate a molecule-optimized basis set whose rank matches that of a standard correlation-consistent basis set optimized for the atoms. We show that basis-set truncation by approximate natural orbitals can be viewed as a one-electron unitary transformation of the Hamiltonian operator and suggest an extension of approximate natural-orbital truncations through two-electron unitary transformations of the Hamiltonian operator, such as those employed in the solution of the ACSE. The molecule-optimized basis set from the ACSE improves the accuracy of the equivalent standard atom-optimized basis set at little additional computational cost. We illustrate the method with the potential energy curves of hydrogen fluoride and diatomic nitrogen. Relative to the hydrogen fluoride potential energy curve from the ACSE in a polarized triple-zeta basis set, the ACSE curve in a molecule-optimized basis set, equivalent in size to a polarized double-zeta basis, has a nonparallelity error of 0.0154 a.u. which is significantly better than the nonparallelity error of 0.0252 a.u. from the polarized double-zeta basis set.

physics.chem-ph↗

arXiv2014

Global Solutions of Hartree-Fock Theory and their Consequences for Strongly Correlated Quantum Systems

We present a density matrix approach for computing global solutions of Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. Equality of the upper- and lower-bound energies guarantees that the computed solution is the globally optimal solution of Hartree-Fock theory. For strongly correlated systems the SDP approach requires us to reassess the accuracy of the Hartree-Fock energies and densities from standard software packages for electronic structure theory. Calculations of the H$_{4}$ dimer and N$_{2}$ molecule show that the energies from SDP Hartree-Fock are lower than those from standard Hartree-Fock methods by 100-200 kcal/mol in the dissociation region. The present findings have important consequences for the computation and interpretation of electron correlation, which is typically defined relative to the Hartree-Fock energy and density.

physics.chem-ph↗

arXiv2013

Effect of Strong Electron Correlation on the Efficiency of Photosynthetic Light Harvesting

Research into the efficiency of photosynthetic light harvesting has focused on two factors: (1) entanglement of chromophores, and (2) environmental noise. While chromophores are conjugated $π$-bonding molecules with strongly correlated electrons, previous models have treated this correlation implicitly without a mathematical variable to gauge correlation-enhanced efficiency. Here we generalize the single-electron/exciton models to a multi-electron/exciton model that explicitly shows the effects of enhanced electron correlation within chromophores on the efficiency of energy transfer. The model provides more detailed insight into the interplay of electron correlation within chromophores and electron entanglement between chromophores. Exploiting this interplay is assisting in the design of new energy-efficient materials, which are just beginning to emerge.

physics.bio-ph↗

arXiv2012

Significant Conditions on the Two-electron Reduced Density Matrix from the Constructive Solution of N-representability

We recently presented a constructive solution to the N-representability problem of the two-electron reduced density matrix (2-RDM)---a systematic approach to constructing complete conditions to ensure that the 2-RDM represents a realistic N-electron quantum system [D. A. Mazziotti, Phys. Rev. Lett. 108, 263002 (2012)]. In this paper we provide additional details and derive further N-representability conditions on the 2-RDM that follow from the constructive solution. The resulting conditions can be classified into a hierarchy of constraints, known as the (2,q)-positivity conditions where the q indicates their derivation from the nonnegativity of q-body operators. In addition to the known T1 and T2 conditions, we derive a new class of (2,3)-positivity conditions. We also derive 3 classes of (2,4)-positivity conditions, 6 classes of (2,5)-positivity conditions, and 24 classes of (2,6)-positivity conditions. The constraints obtained can be divided into two general types: (i) lifting conditions, that is conditions which arise from lifting lower (2,q)-positivity conditions to higher (2,q+1)-positivity conditions and (ii) pure conditions, that is conditions which cannot be derived from a simple lifting of the lower conditions. All of the lifting conditions and the pure (2,q)-positivity conditions for q>3 require tensor decompositions of the coefficients in the model Hamiltonians. Subsets of the new N-representability conditions can be employed with the previously known conditions to achieve polynomially scaling calculations of ground-state energies and 2-RDMs of many-electron quantum systems even in the presence of strong electron correlation.

physics.chem-ph↗

arXiv2012

Structure of Fermionic Density Matrices: Complete N-representability Conditions

We present a constructive solution to the N-representability problem---a full characterization of the conditions for constraining the two-electron reduced density matrix (2-RDM) to represent an N-electron density matrix. Previously known conditions, while rigorous, were incomplete. Here we derive a hierarchy of constraints built upon (i) the bipolar theorem and (ii) tensor decompositions of model Hamiltonians. Existing conditions D, Q, G, T1, and T2, known classical conditions, and new conditions appear naturally. Subsets of the conditions are amenable to polynomial-time computations of strongly correlated systems.

quant-ph↗

arXiv2012

The Impact of Multichannel and Multipole Effects on the Cooper Minimum in the High-Harmonics Spectrum of Argon

We investigate the relevance of multiple-orbital and multipole effects during high-harmonic generation (HHG). The time-dependent configuration-interaction singles (TDCIS) approach is used to study the impact of the detailed description of the residual electron-ion interaction on the HHG spectrum. We find that the shape and position of the Cooper minimum in the HHG spectrum of argon changes significantly whether or not interchannel interactions are taken into account. The HHG yield can be underestimated by up to 2 orders of magnitude in the energy regio of 30-50 eV. We show that the argument of low ionization probability is not sufficient to justify ignoring multiple-orbital contributions. Additionally, we find the HHG yield is sensitive to the nonspherical multipole character of the electron-ion interaction.

physics.atom-ph↗

arXiv2011

Functional Subsystems and Quantum Redundancy in Photosynthetic Light Harvesting

The Fenna-Matthews-Olson (FMO) antennae complex, responsible for light harvesting in green sulfur bacteria, consists of three monomers, each with seven chromophores. Here we show that multiple subsystems of the seven chromophores can transfer energy from either chromophore 1 or 6 to the reaction center with an efficiency matching or in many cases exceeding that of the full seven chromophore system. In the FMO complex these functional subsystems support multiple quantum pathways for efficient energy transfer that provide a built-in quantum redundancy. There are many instances of redundancy in nature, providing reliability and protection, and in photosynthetic light harvesting this quantum redundancy provides protection against the temporary or permanent loss of one or more chromophores. The complete characterization of functional subsystems within the FMO complex offers a detailed map of the energy flow within the FMO complex, which has potential applications to the design of more efficient photovoltaic devices.

physics.bio-ph↗

arXiv2011

Rank Restriction for the Variational Calculation of Two-electron Reduced Density Matrices of Many-electron Atoms and Molecules

Variational minimization of the ground-state energy as a function of the two-electron reduced density matrix (2-RDM), constrained by necessary $N$-representability conditions, provides a polynomial-scaling approach to studying strongly correlated molecules without computing the many-electron wavefunction. Here we introduce a new route to enhancing necessary conditions for $N$-representability through rank restriction of the 2-RDM. Rather than adding computationally more expensive $N$-representability conditions, we directly enhance the accuracy of two-particle (2-positivity) conditions through rank restriction, which removes degrees of freedom in the 2-RDM that are not sufficiently constrained. We select the rank of the particle-hole 2-RDM by deriving the ranks associated with model wavefunctions including both mean-field and antisymmetrized geminal power (AGP) wave functions. Because the 2-positivity conditions are exact for quantum systems with AGP ground states, the rank of the particle-hole 2-RDM from the AGP ansatz provides a minimum for its value in variational 2-RDM calculations of general quantum systems. To implement the rank-restricted conditions, we extend a first-order algorithm for large-scale semidefinite programming. The rank-restricted conditions significantly improve the accuracy of the energies; for example, the percentages of correlation energies recovered for HF, CO, and N$_{2}$ improve from 115.2%, 121.7%, and 121.5% without rank restriction to 97.8%, 101.1%, and 100.0% with rank restriction. Similar results are found at both equilibrium and non-equilibrium geometries. While more accurate, the rank-restricted $N$-representability conditions are less expensive computationally than the full-rank conditions.

quant-ph↗

arXiv2011

Decoherence in Attosecond Photoionization

The creation of superpositions of hole states via single-photon ionization using attosecond extreme-ultraviolet pulses is studied with the time-dependent configuration interaction singles (TDCIS) method. Specifically, the degree of coherence between hole states in atomic xenon is investigated. We find that interchannel coupling not only affects the hole populations, it also enhances the entanglement between the photoelectron and the remaining ion, thereby reducing the coherence within the ion. As a consequence, even if the spectral bandwidth of the ionizing pulse exceeds the energy splittings among the hole states involved, perfectly coherent hole wave packets cannot be formed. For sufficiently large spectral bandwidth, the coherence can only be increased by increasing the mean photon energy.

physics.atom-ph↗

arXiv2010

On the relationship between parametric two-electron reduced-density-matrix methods and the coupled electron pair approximation

Parametric two-electron reduced-density-matrix (p-2RDM) methods have enjoyed much success in recent years; the methods have been shown to exhibit accuracies greater than coupled cluster with single and double substitutions (CCSD) for both closed- and open-shell ground-state energies, properties, geometric parameters, and harmonic frequencies. The class of methods is herein discussed within the context of the coupled electron pair approximation (CEPA), and several CEPA-like topological factors are presented for use within the p-2RDM framework. The resulting p-2RDM/n methods can be viewed as a density-based generalization of CEPA/n family that are numerically very similar to traditional CEPA methodologies. We cite the important distinction that the obtained energies represent stationary points, facilitating the efficient evaluation of properties and geometric derivatives. The p-2RDM/n formalism is generalized for an equal treatment of exclusion-principle-violating (EPV) diagrams that occur in the occupied and virtual spaces. One of these general topological factors is shown to be identical to that proposed by Kollmar [C. Kollmar, J. Chem. Phys. 125, 084108 (2006)], derived in an effort to approximately enforce the D, Q, and G conditions for N-representability in his size-extensive density matrix functional.

physics.chem-ph↗