Ground-state Theory Research Articles

Two-channel thermal transport and scattering channel of high-temperature phase SnSe using temperature-dependent effective potential

To resolve the imaginary phonon frequency of high-temperature phase SnSe (853 K) caused by ground-state theory, the temperature-dependent effective potential (TDEP) method is used to evaluate the temperature-dependent interatomic force constants (IFCs). Based on the Boltzmann transport equation, both two-channel transport and scattering channel are studied using the temperature-dependent IFCs. Considering three-phonon and four-phonon scattering, the particle-like thermal conductivity along the xx axis, yy axis, and zz axis is 0.66, 0.34, and 0.61 W/mK, respectively. For glass-like thermal conductivity, the value along the xx axis, yy axis, zz axis are 0.0777, 0.0316, and 0.0791 W/mK, respectively. For the three-phonon scattering channel, the scattering channels of X + O/A→O and X→O+O/A play a major role. For four-phonon scattering channel, the major scattering channels are X + O+A→O, X + A+A→O, X + O-O/A→A, X + A-O→A, X-O/A-O/A→O, X-O-A→A. By utilizing the crystal orbital Hamilton population (COHP) analysis, the low lattice thermal conductivity is attributed to the weak chemical bonds from anti-bonding orbitals between Se4p and Sn5s states. This work provides new insight into the physical mechanisms for thermal transport of high-temperature phase SnSe with strong anharmonic effects.

Quantum embedding methods for correlated excited states of point defects: Case studies and challenges

A quantitative description of the excited electronic states of point defects and impurities is crucial for understanding materials properties, and possible applications of defects in quantum technologies. This is a considerable challenge for computational methods, since Kohn-Sham density functional theory (DFT) is inherently a ground-state theory, while higher-level methods are often too computationally expensive for defect systems. Recently, embedding approaches have been applied that treat defect states with many-body methods, while using DFT to describe the bulk host material. We implement such an embedding method, based on Wannierization of defect orbitals and the constrained random-phase approximation approach, and perform systematic characterization of the method for three distinct systems with current technological relevance: a carbon dimer replacing a B and N pair in bulk hexagonal BN (${\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}$), the negatively charged nitrogen-vacancy center in diamond (${\mathrm{NV}}^{\ensuremath{-}}$), and an Fe impurity on the Al site in wurtzite AlN (${\text{Fe}}_{\text{Al}}$). In the context of these test-case defects, we demonstrate that crucial considerations of the methodology include convergence of the bulk screening of the active-space Coulomb interaction, the choice of exchange-correlation functional for the initial DFT calculation, and the treatment of the ``double-counting'' correction. For ${\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}$ we show that the embedding approach gives many-body states in agreement with analytical results on the Hubbard dimer model, which allows us to elucidate the effects of the DFT functional and double-counting correction. For the ${\mathrm{NV}}^{\ensuremath{-}}$ center, our method demonstrates good quantitative agreement with experiments for the zero-phonon line of the triplet-triplet transition. Finally, we illustrate challenges associated with this method for determining the energies and orderings of the complex spin multiplets in ${\text{Fe}}_{\text{Al}}$.

Thermal coupled cluster theory for SU(2) systems

Coupled cluster (CC) has established itself as a powerful theory to study correlated quantum many-body systems. Finite-temperature generalizations of CC theory have attracted considerable interest and have been shown to work as nicely as the ground-state theory. However, most of these recent developments address only fermionic or bosonic systems. The distinct structure of the $su(2)$ algebra requires the development of a similar thermal CC theory for spin degrees of freedom. In this paper, we provide a formulation of our thermofield-inspired thermal CC for SU(2) systems. We apply the thermal CC to the Lipkin-Meshkov-Glick system as well as the one-dimensional transverse field Ising model as benchmark applications to highlight the accuracy of thermal CC in the study of finite-temperature phase diagrams in SU(2) systems.

Finite-temperature density matrix embedding theory

We describe a formulation of the density matrix embedding theory at finite temperature. We present a generalization of the ground-state bath orbital construction that embeds a mean-field finite-temperature density matrix up to a given order in the Hamiltonian, or the Hamiltonian up to a given order in the density matrix. We assess the performance of the finite-temperature density matrix embedding on the 1D Hubbard model both at half-filling and away from it, and the 2D Hubbard model at half-filling, comparing to exact data where available, as well as results from finite-temperature density matrix renormalization group, dynamical mean-field theory, and dynamical cluster approximations. The accuracy of finite-temperature density matrix embedding appears comparable to that of the ground-state theory, with at most a modest increase in bath size, and competitive with that of cluster dynamical mean-field theory.

Coordinate Scaling in Time-Independent Excited-State Density Functional Theory for Coulomb Systems

A time-independent density functional theory for excited states of Coulomb systems has recently been proposed in a series of papers. It has been revealed that the Coulomb density determines not only its Hamiltonian, but the degree of excitation as well. A universal functional valid for any excited state has been constructed. The excited-state Kohn–Sham equations bear resemblance to those of the ground-state theory. In this paper, it is studied how the excited-state functionals behave under coordinate scaling. A few relations for the scaled exchange, correlation, exchange-correlation, and kinetic functionals are presented. These relations are expected to be advantageous for designing approximate functionals.

Hartree–Fock many-body perturbation theory for nuclear ground-states

We investigate the order-by-order convergence behavior of many-body perturbation theory (MBPT) as a simple and efficient tool to approximate the ground-state energy of closed-shell nuclei. To address the convergence properties directly, we explore perturbative corrections up to 30th order and highlight the role of the partitioning for convergence. The use of a simple Hartree-Fock solution to construct the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to, e.g., a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation in not feasible, we perform third-order calculation and compare to advanced ab initio coupled-cluster calculations for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into tin isotopic chain that are in excellent agreement with the best available coupled-cluster results at a fraction of the computational cost.

Correction to Multiconfiguration Pair-Density Functional Theory Outperforms Kohn–Sham Density Functional Theory and Multireference Perturbation Theory for Ground-State and Excited-State Charge Transfer

Correction to Multiconfiguration Pair-Density Functional Theory Outperforms Kohn–Sham Density Functional Theory and Multireference Perturbation Theory for Ground-State and Excited-State Charge Transfer

Using DFT Methods to Study Activators in Optical Materials

Density functional theory (DFT) calculations of various activators (ranging from transition metal ions, rare-earth ions, ns2 ions, to self-trapped and dopant-bound excitons) in phosphors and scintillators are reviewed. As a single-particle ground-state theory, DFT calculations cannot reproduce the experimentally observed optical spectra, which involve transitions between multi-electronic states. However, DFT calculations can generally provide sufficiently accurate structural relaxation and distinguish different hybridization strengths between an activator and its ligands in different host compounds. This is important because the activator-ligand interaction often governs the trends in luminescence properties in phosphors and scintillators, which can be used to search for new materials. DFT calculations of the electronic structure of the host compound and the positions of the activator levels relative to the host band edges in scintillators are also important for finding optimal host-activator combinations for high light yields and fast scintillation response. Mn4+ activated red phosphors, scintillators activated by Ce3+, Eu2+, Tl+, and excitons are shown as examples of using DFT calculations in phosphor and scintillator research.

Multiconfiguration Pair-Density Functional Theory Outperforms Kohn-Sham Density Functional Theory and Multireference Perturbation Theory for Ground-State and Excited-State Charge Transfer.

The correct description of charge transfer in ground and excited states is very important for molecular interactions, photochemistry, electrochemistry, and charge transport, but it is very challenging for Kohn-Sham (KS) density functional theory (DFT). KS-DFT exchange-correlation functionals without nonlocal exchange fail to describe both ground- and excited-state charge transfer properly. We have recently proposed a theory called multiconfiguration pair-density functional theory (MC-PDFT), which is based on a combination of multiconfiguration wave function theory with a new type of density functional called an on-top density functional. Here we have used MC-PDFT to study challenging ground- and excited-state charge-transfer processes by using on-top density functionals obtained by translating KS exchange-correlation functionals. For ground-state charge transfer, MC-PDFT performs better than either the PBE exchange-correlation functional or CASPT2 wave function theory. For excited-state charge transfer, MC-PDFT (unlike KS-DFT) shows qualitatively correct behavior at long-range with great improvement in predicted excitation energies.

Embedded correlated wavefunction schemes: theory and applications.

Conspectus Ab initio modeling of matter has become a pillar of chemical research: with ever-increasing computational power, simulations can be used to accurately predict, for example, chemical reaction rates, electronic and mechanical properties of materials, and dynamical properties of liquids. Many competing quantum mechanical methods have been developed over the years that vary in computational cost, accuracy, and scalability: density functional theory (DFT), the workhorse of solid-state electronic structure calculations, features a good compromise between accuracy and speed. However, approximate exchange-correlation functionals limit DFT's ability to treat certain phenomena or states of matter, such as charge-transfer processes or strongly correlated materials. Furthermore, conventional DFT is purely a ground-state theory: electronic excitations are beyond its scope. Excitations in molecules are routinely calculated using time-dependent DFT linear response; however applications to condensed matter are still limited. By contrast, many-electron wavefunction methods aim for a very accurate treatment of electronic exchange and correlation. Unfortunately, the associated computational cost renders treatment of more than a handful of heavy atoms challenging. On the other side of the accuracy spectrum, parametrized approaches like tight-binding can treat millions of atoms. In view of the different (dis-)advantages of each method, the simulation of complex systems seems to force a compromise: one is limited to the most accurate method that can still handle the problem size. For many interesting problems, however, compromise proves insufficient. A possible solution is to break up the system into manageable subsystems that may be treated by different computational methods. The interaction between subsystems may be handled by an embedding formalism. In this Account, we review embedded correlated wavefunction (CW) approaches and some applications. We first discuss our density functional embedding theory, which is formally exact. We show how to determine the embedding potential, which replaces the interaction between subsystems, at the DFT level. CW calculations are performed using a fixed embedding potential, that is, a non-self-consistent embedding scheme. We demonstrate this embedding theory for two challenging electron transfer phenomena: (1) initial oxidation of an aluminum surface and (2) hot-electron-mediated dissociation of hydrogen molecules on a gold surface. In both cases, the interaction between gas molecules and metal surfaces were treated by sophisticated CW techniques, with the remainder of the extended metal surface being treated by DFT. Our embedding approach overcomes the limitations of conventional Kohn-Sham DFT in describing charge transfer, multiconfigurational character, and excited states. From these embedding simulations, we gained important insights into fundamental processes that are crucial aspects of fuel cell catalysis (i.e., O2 reduction at metal surfaces) and plasmon-mediated photocatalysis by metal nanoparticles. Moreover, our findings agree very well with experimental observations, while offering new views into the chemistry. We finally discuss our recently formulated potential-functional embedding theory that provides a seamless, first-principles way to include back-action onto the environment from the embedded region.

Time-independent density-functional theory for excited states of Coulomb systems

A Coulomb density is special because it determines not only its Hamiltonian but the degree of excitation as well. We derive Euler equations for excited-state energies and densities that depend only on the electron density. Unlike existing formulations, additional functions and indices are not required; with these functionals, the equations of excited-state density functional theory strongly resemble those of ground-state theory. A critical analysis of the new functionals is included.

BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures

BerkeleyGW is a massively parallel computational package for electron excited-state properties that is based on the many-body perturbation theory employing the ab initio GW and GW plus Bethe–Salpeter equation methodology. It can be used in conjunction with many density-functional theory codes for ground-state properties, including PARATEC, PARSEC, Quantum ESPRESSO, SIESTA, and Octopus. The package can be used to compute the electronic and optical properties of a wide variety of material systems from bulk semiconductors and metals to nanostructured materials and molecules. The package scales to 10 000s of CPUs and can be used to study systems containing up to 100s of atoms. Program summaryProgram title: BerkeleyGWCatalogue identifier: AELG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELG_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Open source BSD License. See code for licensing details.No. of lines in distributed program, including test data, etc.: 576 540No. of bytes in distributed program, including test data, etc.: 110 608 809Distribution format: tar.gzProgramming language: Fortran 90, C, C++, Python, Perl, BASHComputer: Linux/UNIX workstations or clustersOperating system: Tested on a variety of Linux distributions in parallel and serial as well as AIX and Mac OSXRAM: (50–2000) MB per CPU (Highly dependent on system size)Classification: 7.2, 7.3, 16.2, 18External routines: BLAS, LAPACK, FFTW, ScaLAPACK (optional), MPI (optional). All available under open-source licenses.Nature of problem: The excited state properties of materials involve the addition or subtraction of electrons as well as the optical excitations of electron–hole pairs. The excited particles interact strongly with other electrons in a material system. This interaction affects the electronic energies, wavefunctions and lifetimes. It is well known that ground-state theories, such as standard methods based on density-functional theory, fail to correctly capture this physics.Solution method: We construct and solve the Dysonʼs equation for the quasiparticle energies and wavefunctions within the GW approximation for the electron self-energy. We additionally construct and solve the Bethe–Salpeter equation for the correlated electron–hole (exciton) wavefunctions and excitation energies.Restrictions: The material size is limited in practice by the computational resources available. Materials with up to 500 atoms per periodic cell can be studied on large HPCs.Additional comments: The distribution file for this program is approximately 110 Mbytes and therefore is not delivered directly when download or E-mail is requested. Instead a html file giving details of how the program can be obtained is sent.Running time: 1–1000 minutes (depending greatly on system size and processor number).

T>0ensemble-state density functional theory via Legendre transform

A logical foundation of equilibrium state density functional theory in a Kohn-Sham-type formulation is presented on the basis of Mermin's treatment of the grand canonical state by exploiting functional Legendre transforms. It is simpler and more satisfactory compared to the usual derivation of the ground-state theory and free of most remaining open points of the latter. The existence of the functional derivative of the corresponding density functional $F[n]$ at all densities of grand canonical equilibrium states is proved even in the spin-density matrix version of the theory. It may, in particular, be relevant with respect to cases of spontaneous symmetry breaking such as noncollinear magnetism and orbital order.

Interactions between planar stiff polyelectrolyte brushes

Molecular-dynamics simulations were performed for two opposing flat surfaces sparsely grafted with rigid polyelectrolyte chains whose lengths are smaller than their persistence lengths. The resulting force-distance dependence was analyzed theoretically in terms of two separate physical mechanisms: the pressure arising from osmotically active counterions trapped within the brush and the work required to bend the brush chains under confinement, which can be accurately characterized by a ground-state theory of rigid polymer buckling. These contributions are of the same magnitude and should be distinguishable in experiments of double-stranded DNA brushes.

Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed

Some fundamental issues in ground-state density functional theory are discussed without equations: (1) The standard Hohenberg-Kohn and Kohn-Sham theorems were proven for a Hamiltonian that is not quite exact for real atoms, molecules, and solids. (2) The density functional for the exchange-correlation energy, which must be approximated, arises from the tendency of electrons to avoid one another as they move through the electron density. (3) In the absence of a magnetic field, either spin densities or total electron density can be used, although the former choice is better for approximations. (4) "Spin contamination" of the determinant of Kohn-Sham orbitals for an open-shell system is not wrong but right. (5) Only to the extent that symmetries of the interacting wave function are reflected in the spin densities should those symmetries be respected by the Kohn-Sham noninteracting or determinantal wave function. Functionals below the highest level of approximations should however sometimes break even those symmetries, for good physical reasons. (6) Simple and commonly used semilocal (lower-level) approximations for the exchange-correlation energy as a functional of the density can be accurate for closed systems near equilibrium and yet fail for open systems of fluctuating electron number. (7) The exact Kohn-Sham noninteracting state need not be a single determinant, but common approximations can fail when it is not. (8) Over an open system of fluctuating electron number, connected to another such system by stretched bonds, semilocal approximations make the exchange-correlation energy and hole-density sum rule too negative. (9) The gap in the exact Kohn-Sham band structure of a crystal underestimates the real fundamental gap but may approximate the first exciton energy in the large-gap limit. (10) Density functional theory is not really a mean-field theory, although it looks like one. The exact functional includes strong correlation, and semilocal approximations often overestimate the strength of static correlation through their semilocal exchange contributions. (11) Only under rare conditions can excited states arise directly from a ground-state theory.

Orbital-spin order and the origin of structural distortion inMgTi2O4

We analyze electronic, magnetic, and structural properties of the spinel compound ${\text{MgTi}}_{2}{\text{O}}_{4}$ using the local-density $\text{approximation}+U$ method. We show how ${\text{MgTi}}_{2}{\text{O}}_{4}$ undergoes to a canted orbital-spin ordered state, where charge, spin, and orbital degrees of freedom are frozen in a geometrically frustrated network by electron interactions. In our picture orbital order stabilizes the magnetic ground state and controls the degree of structural distortions. The latter is dynamically derived from the cubic structure in the correlated $\text{LDA}+U$ potential. Our ground-state theory provides a consistent picture for the dimerized phase of ${\text{MgTi}}_{2}{\text{O}}_{4}$, and might be applicable to frustrated materials in general.

Density functional theory of complex transition densities

We present an extension of Hohenberg-Kohn-Sham density functional theory to the domain of complex local potentials and complex electron densities. The approach is applicable to resonance (Siegert) [Phys. Rev. 56, 750 (1939)] states and other scattering and transport problems that can be described by a normalized state of a Hamiltonian containing a complex local potential. Such Hamiltonians are non-Hermitian and their eigenvalues are in general complex, the imaginary part being inversely proportional to the lifetime of the system. The one-to-one correspondence between complex local potentials nu and complex electron densities rho is established provided that the complex variables are sufficiently close to real local potentials and densities of nondegenerate ground states. We show that the exchange-correlation functionals, contributing to the complex energy, are determined through analytic continuation of their ground-state-theory counterparts. This implies that the exchange-correlation effects on the lifetime of a resonance are, under appropriate conditions, already determined by the functionals of the ground-state theory.

Validity of the scaling functional approach for polymer interfaces as a variational theory.

We discuss the soundness of the scaling functional (SF) approach proposed by Aubouy Guiselin and Raphaël [Macromolecules 29, 7261 (1996)] to describe polymeric interfaces. In particular, we demonstrate that this approach is a variational theory. We emphasize the role of SF theory as an important link between ground-state theories suitable to describe adsorbed layers, and "classical" theories for polymer brushes.

Augmented Lagrangian method for order-N electronic structure

Molecular electronic ground-state theories, whether ab initio, or semiempirical are most often formulated as a variational principle, where the electronic ground-state energy, considered a linear or nonlinear functional of a reduced density matrix, obtains a constrained minimum. In this communication, we present a Lagrangian analysis of the self-consistent-field electronic structure problem, which does not resort to the concept of orthogonal molecular orbitals. We also develop a method of constrained minimization efficiently applicable to nonlinear energy functional minimization, as well as to linear models such as tight-binding. The method is able to treat large molecules with an effort that scales linearly with the system size. It has built-in robustness and leads directly to the desired minimal solution. Performance is demonstrated on linear alkane and polyene chains.

Isotope effect on high-pressure behavior of hydrogen-bonded crystals

Abstract A variational correlated ground-state wave-function theory is applied to investigate the high-pressure deformation of hydrogen-bond potential. The effect of deuterium isotope substitution on the quantum-fluctuation-driven phenomena under high hydrostatic pressure is discussed. This model that simultaneously incorporates proton interaction energies and two-state quantum-mechanical tunneling has been applied to the interpretation of high-pressure data in terms of microscopic parameters of a compressed single hydrogen bond. The variation of tunnel splitting and proton interaction energies with pressure for deuterated and undeuterated hydrogen bonds is determined. The theory was employed for predicting and interpreting the pressure dependence of the phase transition temperature for KDP-like ferroelectrics and NQR-frequency coefficients for several deuterated and undeuterated crystals.