68 research outputs found
ROHF Theory Made Simple
Restricted open-shell Hartree-Fock (ROHF) theory is formulated as a projected
self-consistent unrestricted HF (UHF) model by mathematically constraining spin
density eigenvalues. The resulting constrained UHF (CUHF) wave function is
identical to that obtained from Roothaan's effective Fock operator. Our
and CUHF Fock operators are parameter-free and have canonical
orbitals and orbital energies that are physically meaningful as in UHF, except
for eliminating spin contamination. The present approach removes ambiguities in
ROHF orbital energies and the non-uniqueness of methods that build upon them.
We present benchmarks to demonstrate CUHF physical correctness and good
agreement with experimental results
Extended M{\o}ller-Plesset perturbation theory for dynamical and static correlations
We present a novel method that appropriately handles both dynamical and
static electron correlation in a balanced manner, using a perturbation theory
on a spin-extended Hartree-Fock (EHF) wave function reference. While EHF is a
suitable candidate for degenerate systems where static correlation is
ubiquitous, it is known that most of dynamical correlation is neglected in EHF.
In this work, we derive a perturbative correction to a fully spin-projected
self-consistent wave function based on second-order M{\o}ller-Plesset
perturbation theory (MP2). The proposed method efficiently captures the ability
of EHF to describe static correlation in degeneracy, combined with MP2's
ability to treat dynamical correlation effects. We demonstrate drastic
improvements on molecular ground state and excited state potential energy
curves and singlet-triplet splitting energies over both EHF and MP2 with
similar computational effort to the latter.Comment: 5 pages, 3 figures, 2 table
Describing strong correlations with mean-field approximations
Strong electron correlations in electronic structure theory are purely quantum effects arising as a result of degeneracies in molecules and materials, and exhibit significantly different yet interesting characters than do weak correlations. Although weak correlations have recently been able to be described very efficiently and accurately within single particle pictures, less known are good prescriptions for treating strong correlations efficiently. Brute-force calculations of strong correlations in wave
function theories tend to be very computationally-intensive, and are usually limited to small molecules for applications.
Breaking symmetry in a mean-field approximation is an efficient alternative to acquire strong correlations with, in many cases, qualitatively accurate results. The
symmetry broken in quantum chemistry has been traditionally of spin, in so-called unrestricted methods, which typically break spatial symmetry as a consequence, and vice versa, in most situations. In this work, we present a novel approach to accurately describing strong correlations with a mean-field cost by means of Hartree-
Fock-Bogoliubov (HFB) theory. We are inspired by the number-symmetry-breaking in HFB, which, with an attractive particle interaction, accounts for strong correlations, while maintaining spin and spatial symmetry. We show that this attractive interaction must be restricted to the chemically-relevant orbitals in an active space to obtain physically meaningful results. With such constraints, our constrained pairing mean-field theory (CPMFT) can accurately describe potential energy curves of various strongly-correlated molecular systems, by cleanly separating strong and weak correlations. To achieve the correct dissociation limits in hetero-atomic molecules, we have modified our CPMFT functional by adding asymptotic constraints. We also include weak correlations by combining CPMFT with density functional theory for chemically accurate results, and reveal the connection between CPMFT and traditional unrestricted methods.
The similarity between CPMFT and unrestricted methods leads us to the idea of constrained active space unrestricted mean-field approaches. Motivated by CPMFT, we partially retrieve spin-symmetry that has been fully broken in unrestricted methods. We allow symmetry breaking only in an active space. This constrained unrestricted Hartree-Fock (CUHF) is an interpolation between two extrema: the fully broken-symmetry solution and the symmetry preserved solution. This thesis defines the theory behind and reports the results of CUHF. We first show that, if an active space is chosen to include only open-shell electrons, CUHF reduces to restricted open-shell Hartree-Fock (ROHF), and such CUHF proves in many ways significantl
Improved algorithms of quantum imaginary time evolution for ground and excited states of molecular systems
Quantum imaginary time evolution (QITE) is a recently proposed
quantum-classical hybrid algorithm that is guaranteed to reach the lowest state
of system. In this study, we present several improvements on QITE, mainly
focusing on molecular applications. We analyze the derivation of the underlying
QITE equation order-by-order, and suggest a modification that is theoretically
well founded. Our results clearly indicate the soundness of the here-derived
equation, enabling a better approximation of the imaginary time propagation by
a unitary. We also discuss how to accurately estimate the norm of an
imaginary-time-evolved state, and applied it to excited state calculations
using the quantum Lanczos algorithm. Finally, we propose the folded-spectrum
QITE scheme as a straightforward extension of QITE for general excited state
simulations. The effectiveness of all these developments is illustrated by
noiseless simulations, offering the further insights into quantum algorithms
for imaginary time evolution.Comment: 10 pages, 5 figures, 1 tabl
Spin-projection for quantum computation: A low-depth approach to strong correlation
Although spin is a core property in fermionic systems, its symmetry can be
easily violated in a variational simulation, especially when strong correlation
plays a vital role therein. In this study, we will demonstrate that the broken
spin-symmetry can be restored exactly in a quantum computer, with little
overhead in circuits, while delivering additional strong correlation energy
with the desired spin quantum number. The proposed scheme permits drastic
reduction of a potentially large number of measurements required to ensure
spin-symmetry by employing a superposition of only a few rotated quantum
states. Our implementation is universal, simple, and, most importantly,
straightforwardly applicable to any ansatz proposed to date.Comment: 9 pages, 7 figures, 2 table
Analytic energy gradients for constrained DFT-configuration interaction
The constrained density functional theory-configuration interaction (CDFT-CI) method has previously been used to calculate ground-state energies and barrier heights, and to describe electronic excited states, in particular conical intersections. However, the method has been limited to evaluating the electronic energy at just a single nuclear configuration, with the gradient of the energy being available only via finite difference. In this paper, we present analytic gradients of the CDFT-CI energy with respect to nuclear coordinates, which gives the potential for accurate geometry optimization and molecular dynamics on both the ground and excited electronic states, a realm which is currently quite challenging for electronic structure theory. We report the performance of CDFT-CI geometry optimization for representative reaction transition states as well as molecules in an excited state. The overall accuracy of CDFT-CI for computing barrier heights is essentially unchanged whether the energies are evaluated at geometries obtained from quadratic configuration-interaction singles and doubles (QCISD) or CDFT-CI, indicating that CDFT-CI produces very good reaction transition states. These results open up tantalizing possibilities for future work on excited states.National Science Foundation (U.S.) (CAREER Award CHE-0547877)David & Lucile Packard Foundation (Fellowship
Many-Body-Expansion Based on Variational Quantum Eigensolver and Deflation for Dynamical Correlation
In this study, we utilize the many-body expansion (MBE) framework to
decompose electronic structures into fragments by incrementing the virtual
orbitals. Our work aims to accurately solve the ground and excited state
energies of each fragment using the variational quantum eigensolver and
deflation algorithms. Although our approach is primarily based on unitary
coupled cluster singles and doubles (UCCSD) and a generalization thereof, we
also introduce modifications and approximations to conserve quantum resources
in MBE by partially generalizing the UCCSD operator and neglecting the
relaxation of the reference states. As a proof of concept, we investigate the
potential energy surfaces for the bond-breaking processes of the ground state
of two molecules ( and ) and calculate the ground and
excited state energies of three molecules (LiH, CH, and ). The
results demonstrate that our approach can, in principle, provide reliable
descriptions in all tests, including strongly correlated systems, when
appropriate approximations are chosen. Additionally, we perform model
simulations to investigate the impact of shot noise on the total MBE energy and
show that precise energy estimation is crucial for lower-order MBE fragments
Adaptive construction of shallower quantum circuits with quantum spin projection for fermionic systems
Quantum computing is a promising approach to harnessing strong correlation in
molecular systems; however, current devices only allow for hybrid
quantum-classical algorithms with a shallow circuit depth, such as the
variational quantum eigensolver (VQE). In this study, we report the importance
of the Hamiltonian symmetry in constructing VQE circuits adaptively. This
treatment often violates symmetry, thereby deteriorating the convergence of
fidelity to the exact solution, and ultimately resulting in deeper circuits. We
demonstrate that symmetry-projection can provide a simple yet effective
solution to this problem, by keeping the quantum state in the correct symmetry
space, to reduce the overall gate operations. The scheme also reveals the
significance of preserving symmetry in computing molecular properties, as
demonstrated in our illustrative calculations
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