Conventional Electronic Structure Methods Research Articles

Quantum computing for electronic structure analysis: Ground state energy and molecular properties calculations

The computation of electronic structure properties at the quantum level is a crucial aspect of modern physics research. However, conventional methods can be computationally demanding for larger, more complex systems. To address this issue, we present a hybrid Classical-Quantum computational procedure that uses the Variational Quantum Eigensolver (VQE) algorithm. By mapping the quantum system to a set of qubits and utilising a quantum circuit to prepare the ground state wavefunction, our algorithm offers a streamlined process requiring fewer computational resources than classical methods. Our algorithm demonstrated similar accuracy in rigorous comparisons with conventional electronic structure methods, such as Density Functional Theory and Hartree–Fock Theory, on a range of molecules while utilising significantly fewer resources. These results indicate the potential of the algorithm to expedite the development of new materials and technologies. This work paves the way for overcoming the computational challenges of electronic structure calculations. It demonstrates the transformative impact of quantum computing on advancing our understanding of complex quantum systems.

Efficient Calculation of NMR Shielding Constants Using Composite Method Approximations and Locally Dense Basis Sets.

This paper presents a systematic study of applying composite method approximations with locally dense basis sets (LDBS) to efficiently calculate NMR shielding constants in small and medium-sized molecules. The pcSseg-n series of basis sets are shown to have similar accuracy to the pcS-n series when n ≥ 1 and can slightly reduce computational costs. We identify two different LDBS partition schemes that perform very effectively for density functional calculations. We select a large subset of the recent NS372 database containing 290 H, C, N, and O shielding values evaluated by reference methods on 106 molecules to carefully assess methods of the high, medium, and low computational costs to make practical recommendations. Our assessment covers conventional electronic structure methods (density functional theory and wave function) with global basis calculations, as well as their use in one of the satisfactory LDBS approaches, and a range of composite approaches, also with and without LDBS. Altogether 99 methods are evaluated. On this basis, we recommend different methods to reach three different levels of accuracy and time requirements across the four nuclei considered.

Electronic Properties of Hexagonal Graphene Quantum Rings from TAO-DFT.

The reliable prediction of electronic properties associated with graphene nanosystems can be challenging for conventional electronic structure methods, such as Kohn-Sham (KS) density functional theory (DFT), due to the presence of strong static correlation effects in these systems. To address this challenge, TAO (thermally assisted occupation) DFT has been recently proposed. In the present study, we employ TAO-DFT to predict the electronic properties of n-HGQRs (i.e., the hexagonal graphene quantum rings consisting of n aromatic rings fused together at each side). From TAO-DFT, the ground states of n-HGQRs are singlets for all the cases investigated (n = 3-15). As the system size increases, there should be a transition from the nonradical to polyradical nature of ground-state n-HGQR. The latter should be intimately related to the localization of active TAO-orbitals at the inner and outer edges of n-HGQR, which increases with increasing system size.

Effective Fragment Potentials for Microsolvated Excited and Anionic States.

The effective fragment potential (EFP) approach is a sophisticated hybrid approach that allows the inclusion of solvation effects when describing properties and reactivity in the condensed phase, without using empirical parameters. This work examines the performance of the EFP method when describing microsolvation in electronically excited states of neutrals and anions. The examples selected include both localized valence states, as well as diffuse nonvalence states, which represent greater challenges to conventional electronic structure methods. The equation-of-motion coupled cluster with singles and doubles (EOM-XX-CCSD) methodology has been used to provide the quantum chemical description of both the full microsolvated clusters, and the chromophoric moiety in mixed quantum/EFP calculations. We find that, when averaging over multiple configurations of microsolvated clusters, the differences between QM/EFP and full quantum results are minimal, although individual configurations often have larger errors. As expected, diffuse states have somewhat larger errors, although not significantly so. The close proximity of states leading to mixing can make QM/EFP less accurate because a change of ordering of states can occur. Other properties, such as photoelectron images and lifetimes of metastable states, are very well described for the monohydrated clusters investigated.

Solution of two-electron Schrödinger equations using a residual minimization method and one-dimensional basis functions

Distinctive from conventional electronic structure methods, we solve the Schrödinger wave equations of the helium atom and its isoelectronic ions by employing one-dimensional basis functions to separate components. We use full two-electron six-dimensional operators and wavefunctions represented with real-space grids where the refinement of the latter is carried out using a residual minimization method. In contrast to the standard single-electron approach, the current approach results in exact treatment of repulsion energy and, hence, more accurate electron correlation within five centihartrees or better included, with moderate computational cost. A simple numerical convergence between the error to accurate results and the grid-spacing size is found. The obtained two-electron Schrödinger wavefunction that contains vast and elaborating information for the radial correlation function and common one-dimensional functions shows the electron correlation effect on one-electron distributions.

TAO-DFT-Based Ab Initio Molecular Dynamics.

Recently, AIMD (ab initio molecular dynamics) has been extensively employed to explore the dynamical information of electronic systems. However, it remains extremely challenging to reliably predict the properties of nanosystems with a radical nature using conventional electronic structure methods (e.g., Kohn-Sham density functional theory) due to the presence of static correlation. To address this challenge, we combine the recently formulated TAO-DFT (thermally-assisted-occupation density functional theory) with AIMD. The resulting TAO-AIMD method is employed to investigate the instantaneous/average radical nature and infrared spectra of n-acenes containing n linearly fused benzene rings (n = 2–8) at 300 K. According to the TAO-AIMD simulations, on average, the smaller n-acenes (up to n = 5) possess a nonradical nature, and the larger n-acenes (n = 6–8) possess an increasing radical nature, showing remarkable similarities to the ground-state counterparts at 0 K. Besides, the infrared spectra of n-acenes obtained with the TAO-AIMD simulations are in qualitative agreement with the existing experimental data.

TAO-DFT investigation of electronic properties of linear and cyclic carbon chains

It has been challenging to adequately investigate the properties of nanosystems with radical nature using conventional electronic structure methods. We address this challenge by calculating the electronic properties of linear carbon chains (l-CC[n]) and cyclic carbon chains (c-CC[n]) with n = 10–100 carbon atoms, using thermally-assisted-occupation density functional theory (TAO-DFT). For all the cases investigated, l-CC[n]/c-CC[n] are ground-state singlets, and c-CC[n] are energetically more stable than l-CC[n]. The electronic properties of l-CC[n]/c-CC[n] reveal certain oscillation patterns for smaller n, followed by monotonic changes for larger n. For the smaller carbon chains, odd-numbered l-CC[n] are more stable than the adjacent even-numbered ones; c-CC[4m+2]/c-CC[4m] are more/less stable than the adjacent odd-numbered ones, where m are positive integers. As n increases, l-CC[n]/c-CC[n] possess increasing polyradical nature in their ground states, where the active orbitals are delocalized over the entire length of l-CC[n] or the whole circumference of c-CC[n].

Trajectory surface hopping molecular dynamics simulation by spin-flip time-dependent density functional theory.

This paper presents the nonadiabatic molecular dynamics simulation combined with the spin-flip time-dependent density functional theory (SF-TDDFT). In contrast to the conventional single-reference electronic structure methods, which have difficulty in describing the S0/S1 conical intersections, the SF-TDDFT can yield the correct topology of crossing points. Thus, one expects that the method can take naturally into account the S1 → S0 nonadiabatic transitions. We adopt Tully's fewest switch surface hopping algorithm by introducing the analytic SF-TDDFT nonadiabatic coupling vector. We apply the proposed method to the photoisomerization reactions of E-azomethane, methanimine, and ethene molecules and reproduce the results of previous studies based on the multireference methods. The proposed approach overcomes the ad hoc treatment of S1 → S0 transition at the single-reference calculation level and affords both the dynamics on the S1 state and the recovery of the S0 state with modest computational costs.

Targeting Doubly Excited States with Equation of Motion Coupled Cluster Theory Restricted to Double Excitations.

The accurate description of doubly excited states using conventional electronic structure methods is remarkably challenging, primarily because such excited states require the inclusion of doubly or higher excited configurations or the application of multireference methods. We present a new approach to target electronically excited states that feature a double-electron transfer. Our method uses the equation of motion (EOM) formalism with a pair coupled cluster doubles (pCCD) reference function, where dynamical correlation is accounted for by a linearized coupled cluster correction with singles and doubles (LCCSD). Specifically, our proposed EOM-pCCD-LCCSD model represents a simplification of the conventional EOM-CCSD approach, where the electron-pair amplitudes of CCSD are tailored by pCCD. The performance of EOM-pCCD-LCCSD is assessed for the lowest-lying excited states in CH+ and all-trans polyenes. In contrast to conventional EOM-CC methods with at most double excitations, EOM-pCCD-LCCSD predicts the right order of states in polyenes with excitation energies closest to experiment, outperforming even highly accurate methods such as the density matrix renormalization group algorithm.

Controlled-Potential Simulation of Elementary Electrochemical Reactions: Proton Discharge on Metal Surfaces

The simulation of electrochemical reaction dynamics from first principles remains challenging, since over the course of an elementary step, an electron is either consumed or produced by the electrode. For example, the hydrogen evolution reaction begins with a simple proton discharge to a metal surface, but with conventional electronic structure methods, the simulated potential, which is manifested as the metal’s workfunction, varies over the course of the simulation as the electron is consumed in the new metal–hydrogen bond. Here, we present a simple approach to allow the direct control of the electrochemical potential via charging of the electrode surface. This is achieved by changing the total number of electrons in the self-consistent cycle, while enforcing charge neutrality through the introduction of a jellium counter charge dispersed in an implicit solvent region above the slab. We observe that the excess electrons localize selectively at the metal’s reactive surface and that the metal workfunction ...

Calculating potential energy curves with fixed-node diffusion Monte Carlo: CO and N2.

This study reports on the prospect for the routine use of Quantum Monte Carlo (QMC) for the electronic structure problem, applying fixed-node Diffusion Monte Carlo (DMC) to generate highly accurate Born-Oppenheimer potential energy curves (PECs) for small molecular systems. The singlet ground electronic states of CO and N2 were used as test cases. The PECs obtained by DMC employing multiconfigurational trial wavefunctions were compared with those obtained by conventional high-accuracy electronic structure methods such as multireference configuration interaction and/or the best available empirical spectroscopic curves. The goal was to test whether a straightforward procedure using available QMC codes could be applied robustly and reliably. Results obtained with DMC codes were found to be in close agreement with the benchmark PECs, and the n3 scaling with the number of electrons (compared with n7 or worse for conventional high-accuracy quantum chemistry) could be advantageous depending on the system size. Due to a large pre-factor in the scaling, for the small systems tested here, it is currently still much more computationally intensive to compute PECs with QMC. Nevertheless, QMC algorithms are particularly well-suited to large-scale parallelization and are therefore likely to become more relevant for future massively parallel hardware architectures.

Effect of Li Adsorption on the Electronic and Hydrogen Storage Properties of Acenes: A Dispersion-Corrected TAO-DFT Study

Due to the presence of strong static correlation effects and noncovalent interactions, accurate prediction of the electronic and hydrogen storage properties of Li-adsorbed acenes with n linearly fused benzene rings (n = 3–8) has been very challenging for conventional electronic structure methods. To meet the challenge, we study these properties using our recently developed thermally-assisted-occupation density functional theory (TAO-DFT) with dispersion corrections. In contrast to pure acenes, the binding energies of H2 molecules on Li-adsorbed acenes are in the ideal binding energy range (about 20 to 40 kJ/mol per H2). Besides, the H2 gravimetric storage capacities of Li-adsorbed acenes are in the range of 9.9 to 10.7 wt%, satisfying the United States Department of Energy (USDOE) ultimate target of 7.5 wt%. On the basis of our results, Li-adsorbed acenes can be high-capacity hydrogen storage materials for reversible hydrogen uptake and release at ambient conditions.

Electronic Properties of III-V Semiconductor Photocathode-Water Interfaces: Predictions from First-Principles Calculations

Photoelectrochemical (PEC) cells based on III-V semiconductor photocathodes offer a promising avenue for hydrogen production from water and sunlight. The efficiency of these devices depends on the electronic structure of the interface between the photocathode and liquid water, including the alignment between the semiconductor band edges and the water redox potential. Accurate theoretical predictions of this quantity remain a challenging task, as conventional electronic structure methods such as density functional theory (DFT) often yield substantial errors [1]. In this talk, we present calculations of the electronic properties of two representative III-V semiconductor electrodes, i.e. GaP and InP, at the interface with water using a combination of first-principles molecular dynamics simulations and many-body perturbation theory (MBPT). We show that the use of MBPT is key to obtain band alignments in agreement with experimental measurements. In addition, we describe the relationship between interfacial structure, electronic properties of semiconductors and their reactivity in aqueous solutions. 1. T. A. Pham, D. Lee, E. Schwegler and G. Galli, J. Am. Chem. Soc. in press (2014). This work was supported by the U.S. Department of Energy at the Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Electronic Properties of Zigzag Graphene Nanoribbons Studied by TAO-DFT.

Accurate prediction of the electronic properties of zigzag graphene nanoribbons (ZGNRs) has been very challenging for conventional electronic structure methods due to the presence of strong static correlation effects. To meet the challenge, we study the singlet-triplet energy gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, and symmetrized von Neumann entropy (i.e., a measure of polyradical character) of hydrogen-terminated ZGNRs with different widths and lengths using our recently developed thermally-assistedoccupation density functional theory (TAO-DFT) [Chai, J.-D. J. Chem. Phys. 2012, 136, 154104], a very efficient method for the study of large strongly correlated systems. Our results are in good agreement with the available experimental and high-accuracy ab initio data. The ground states of ZGNRs are shown to be singlets for all the widths and lengths investigated. With the increase of ribbon length, the singlet-triplet energy gaps, vertical ionization potentials, and fundamental gaps decrease monotonically, while the vertical electron affinities and symmetrized von Neumann entropy increase monotonically. On the basis of the calculated orbitals and their occupation numbers, the longer ZGNRs are shown to possess increasing polyradical character in their ground states, where the active orbitals are mainly localized at the zigzag edges.

Thermally-assisted-occupation density functional theory with generalized-gradient approximations

We extend the recently proposed thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)] to generalized-gradient approximation (GGA) exchange-correlation density functionals. Relative to our previous TAO-LDA (i.e., the local density approximation to TAO-DFT), the resulting TAO-GGAs are significantly superior for a wide range of applications, such as thermochemistry, kinetics, and reaction energies. For noncovalent interactions, TAO-GGAs with empirical dispersion corrections are shown to yield excellent performance. Due to their computational efficiency for systems with strong static correlation effects, TAO-LDA and TAO-GGAs are applied to study the electronic properties (e.g., the singlet-triplet energy gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, and symmetrized von Neumann entropy) of acenes with different number of linearly fused benzene rings (up to 100), which is very challenging for conventional electronic structure methods. The ground states of acenes are shown to be singlets for all the chain lengths studied here. With the increase of acene length, the singlet-triplet energy gaps, vertical ionization potentials, and fundamental gaps decrease monotonically, while the vertical electron affinities and symmetrized von Neumann entropy (i.e., a measure of polyradical character) increase monotonically.

Negative electron affinities from conventional electronic structure methods

If the potential V describing the interaction between an excess electron and a ground-state neutral or anionic parent is sufficiently attractive at short range, electron-attached states having positive electron affinities (EAs) can arise. Even if the potential is not attractive enough to produce a bound state, metastable electron-attached states may still occur and have lifetimes long enough to give rise to experimentally detectable signatures. Low-energy metastable states arise when the attractive components of V combine with a longer-range repulsive contribution to produce a barrier behind which the excess electron can be temporarily trapped. These repulsive contributions arise from either the centrifugal potential in the excess electron’s angular kinetic energy or long-range Coulomb repulsion in the case of an anionic parent. When there is no barrier, this kind of low-energy metastable state does not arise, but improper theoretical calculations can lead to erroneous predictions of their existence. Conventional electronic structure methods with, at most, minor modifications are described for properly characterizing metastable states and for avoiding incorrectly predicting the existence of metastable states with negative EAs where no barrier is present.

The Effective Fragment Molecular Orbital Method for Fragments Connected by Covalent Bonds

We extend the effective fragment molecular orbital method (EFMO) into treating fragments connected by covalent bonds. The accuracy of EFMO is compared to FMO and conventional ab initio electronic structure methods for polypeptides including proteins. Errors in energy for RHF and MP2 are within 2 kcal/mol for neutral polypeptides and 6 kcal/mol for charged polypeptides similar to FMO but obtained two to five times faster. For proteins, the errors are also within a few kcal/mol of the FMO results. We developed both the RHF and MP2 gradient for EFMO. Compared to ab initio, the EFMO optimized structures had an RMSD of 0.40 and 0.44 Å for RHF and MP2, respectively.

Density functional theory with fractional orbital occupations

In contrast to the original Kohn-Sham (KS) formalism, we propose a density functional theory (DFT) with fractional orbital occupations for the study of ground states of many-electron systems, wherein strong static correlation is shown to be described. Even at the simplest level represented by the local density approximation (LDA), our resulting DFT-LDA is shown to improve upon KS-LDA for multi-reference systems, such as dissociation of H(2) and N(2), and twisted ethylene, while performing similar to KS-LDA for single-reference systems, such as reaction energies and equilibrium geometries. Because of its computational efficiency (similar to KS-LDA), this DFT-LDA is applied to the study of the singlet-triplet energy gaps (ST gaps) of acenes, which are "challenging problems" for conventional electronic structure methods due to the presence of strong static correlation effects. Our calculated ST gaps are in good agreement with the existing experimental and high-level ab initio data. The ST gaps are shown to decrease monotonically with the increase of chain length, and become vanishingly small (within 0.1 kcal/mol) in the limit of an infinitely large polyacene. In addition, based on our calculated active orbital occupation numbers, the ground states for large acenes are shown to be polyradical singlets.

Tensor Product Multiscale Many-Particle Spaces with Finite-Order Weights for the Electronic Schrödinger Equation

Abstract In this article we combine the favorable properties of efficient Gaussian type orbitals basis sets, which are applied with good success in conventional electronic structure methods, and tensor product multiscale bases, which provide guaranteed convergence rates and allow for adaptive resolution. To this end, we develop and study a new approach for the treatment of the electronic Schrödinger equation based on a modified adaptive sparse grid technique and a certain particle-wise decomposition with respect to one-particle functions obtained by a nonlinear rank-1 approximation. Here, we employ a multiscale Gaussian frame for the sparse grid spaces and we use Gaussian type orbitals to represent the rank-1 approximation. With this approach we are able to treat small atoms and molecules with up to six electrons.

Role of Atomic Multiplets in the Electronic Structure of Rare-Earth Semiconductors and Semimetals

We present a study of the effects of strong correlations in rare-earth pnictides, in which localized 4f states simultaneously retain atomiclike character and strongly influence the free-electron-like valence electron states. Using erbium arsenide as our example, we use a modern implementation of dynamical mean-field theory to obtain the atomic multiplet structure of the Er3+ 4f shell, as well as its unusually strong coupling to the electronic Fermi surfaces; these types of behavior are not correctly described within conventional electronic-structure methods. We are then able to explain the long-standing theoretical question of the quasisaturation of magnetization in an applied magnetic field, and to obtain the first quantitative agreement with experimental Shubnikov-de Haas frequencies of the Fermi-surface sheets.