Configuration Interaction Hamiltonian Research Articles

Multiconfigurational Correlation at DFT + U Cost: On-Site Electron-Electron Interactions Yield a Block-Localized Configuration Interaction Hamiltonian.

This work presents a first-principles wavefunction-in-DFT approach based on the Hubbard density functional theory (DFT) + U method. This approach begins with the standard DFT reference system of noninteracting electrons and introduces an electron-electron interaction projected onto DFT+U-type atomic states. The reference system's configuration interaction Hamiltonian is block-localized to these states and can be expressed in terms of state occupation numbers, state self-energies (which correspond to unscreened Hubbard U values), and the promotion energies of doubly excited Slater determinants. Simple approximations for the promotion energies provide multiconfigurational correlation energies without requiring explicit orbital localization/transform. Numerical results for fractionally occupied chromium atom, bonded chromium dimer, dissociating covalent bonds, and large active spaces show that the approach provides beyond-zero-sum accuracy at computational cost comparable to standard DFT+U.

Electronic Structure for Multielectronic Molecules near a Metal Surface

We analyze a model problem representing a multielectronic molecule sitting on a metal surface. Working with a reduced configuration interaction Hamiltonian, we show that one can extract very accurate ground state wave functions as compared with numerical renormalization group theory (NRG)—even in the limit of weak metal-molecule coupling strength but strong intramolecular electron–electron repulsion. Moreover, we extract what appear to be meaningful excitation energies as well. Our findings should lay the groundwork for future ab initio studies of charge transfer processes and bond making/breaking processes on metal surfaces.

Least action and the maximum-coupling approximations in the theory of spontaneous fission

We investigate the dynamics of spontaneous fission in a configuration-interaction (CI) approach. In that formalism the decay rate is governed by an effective interaction coupling the ground-state configuration and a fission doorway configuration, with the interaction strength determined by inverting a high-dimensioned CI Hamiltonian matrix that may have a block-tridiagonal structure. It is shown that the decay rate decreases exponentially with the number of blocks at a rate determined by the largest eigenvalue of a matrix in the block space for Hamiltonians with identical off-diagonal blocks. The theory is greatly simplified by approximations similar in spirit to the adiabatic and the least-action approximations in continuum representations. Here each block is replaced by a single matrix element. While the adiabatic reduction underestimates the coupling, a reduction based on a maximum-coupling approximation works well in a schematic CI model.

The Simplest Possible Approach for Simulating S0- S1 Conical Intersections with DFT/TDDFT: Adding One Doubly Excited Configuration.

A simple combination of density functional theory/time-dependent density functional theory (DFT/TDDFT) and configuration interaction is presented to fix the incorrect topology of the S0- S1 conical intersection (CI) and allow a description of bond making and bond breaking in photoinduced dynamics. The proposed TDDFT-1D method includes one lone optimized doubly excited configuration in addition to the DFT/TDDFT singly excited states within the context of a large configuration interaction Hamiltonian. Results for ethylene and stilbene are provided to demonstrate that this ansatz can yield physically meaningful potential energy surfaces near S0- S1 avoided crossings without changing the vertical excitation energies far from the relevant crossings. We also investigate the famous linear water example to show that the algorithm calculates the correct topology of the S0- S1 CI and yields the correct geometric phase.

Dynamical configuration interaction: Quantum embedding that combines wave functions and Green's functions

We present the concept, derivation, and implementation of dynamical configuration interaction, a quantum embedding theory that combines Green's function methodology with the many-body wave function. In a strongly correlated active space, we use full configuration interaction (CI) to describe static correlation exactly. We add energy-dependent corrections to the CI Hamiltonian which, in principle, include all remaining correlations derived from the bath space surrounding the active space. Next, we replace the exact Hamiltonian in the bath with one of excitations defined over a correlated ground state. This transformation is naturally suited to the methodology of many-body Green's functions. In this space, we use a modified $GW$/Bethe-Salpeter equation procedure to calculate excitation energies. Combined with an estimate of the ground-state energy in the bath, we can efficiently compute the energy-dependent corrections, which correlate the full set of orbitals, for very low computational cost. We present dimer dissociation curves for ${\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}$ in good agreement with exact results. Additionally, excited states of ${\mathrm{N}}_{2}$ and ${\mathrm{C}}_{2}$ are in excellent agreement with benchmark theory and experiment. By combining the strengths of two disciplines, we achieve a balanced description of static and dynamic correlation in a fully ab initio, systematically improvable framework.

Influence of dielectric environment on exciton and bi-exciton properties in colloidal, type II quantum dots

We present theoretical calculations of type II CdSe/CdTe quantum dots systems. We use an 8-band k.p Hamiltonian that includes spin-orbit interaction, strain, and first order piezoelectric effects. Exciton and bi-exciton states are found using the configuration interaction (CI) method that explicitly includes the effects of the Coulomb interaction, as well as exchange and correlation effects between many-electron configurations. We study convergence of the CI Hamiltonian with respect to the number of single particle states used in creation of the Hamiltonian. We show that there is a very strong correlation between the dielectric constant of the environment and exciton and bi-exciton energies.

Strain effects on optical properties of tetrapod-shaped CdTe/CdS core–shell nanocrystals

The exciton states of strained CdTe/CdS core–shell tetrapod-shaped nanocrystals were theoretically investigated by the numerical diagonalization of a configuration interaction Hamiltonian based on the single-band effective mass approximation. We found that the inclusion of strain promotes the type-II nature by confining the electrons and holes in nonadjacent regions. This carrier separation is more efficient than that with type-II spherical nanocrystals. The strain leads to a small blue shift of the lowest exciton energy. Its magnitude is smaller than the red shift induced by increasing the shell thickness. Moreover, the larger arm diameter reduces the influence of both shell thickness and strain on the exciton energy. Considering the broken symmetry, a randomness induced carrier separation was revealed which is unique to a branched core–shell structure. The calculated shell thickness dependence of the emission energy agrees well with available experimental data.

Exciton states of II–VI tetrapod-shaped nanocrystals

Excitons of tetrapod-shaped nanocrystals made of CdTe, CdS, CdSe, ZnTe, and ZnSe were investigated systematically by numerical diagonalization of configuration interaction Hamiltonian based on single-particle states obtained by finite-element method. Both one-particle and exciton wave functions have high spatial symmetries due to the tetrahedral symmetry of the nanocrystals, which leads to a distinct selection rule for optical absorption and emission. The absorption spectra thus calculated were compared with available experimental data and good agreement was found.

Ab initio derivation of multi-orbital extended Hubbard model for molecular crystals

From configuration interaction (CI) ab initio calculations, we derive an effective two-orbital extended Hubbard model based on the gerade (g) and ungerade (u) molecular orbitals (MOs) of the charge-transfer molecular conductor (TTM-TTP)I(3) and the single-component molecular conductor [Au(tmdt)(2)]. First, by focusing on the isolated molecule, we determine the parameters for the model Hamiltonian so as to reproduce the CI Hamiltonian matrix. Next, we extend the analysis to two neighboring molecule pairs in the crystal and we perform similar calculations to evaluate the inter-molecular interactions. From the resulting tight-binding parameters, we analyze the band structure to confirm that two bands overlap and mix in together, supporting the multi-band feature. Furthermore, using a fragment decomposition, we derive the effective model based on the fragment MOs and show that the staking TTM-TTP molecules can be described by the zig-zag two-leg ladder with the inter-molecular transfer integral being larger than the intra-fragment transfer integral within the molecule. The inter-site interactions between the fragments follow a Coulomb law, supporting the fragment decomposition strategy.

Exciton states of CdTe tetrapod-shaped nanocrystals

Excitons of CdTe tetrapod-shaped nanocrystals are theoretically analyzed. Individual electron and hole states are calculated by solving one-particle Schrodinger equation by the finite element method with the single-band effective-mass approximation and exciton states are obtained by numerical diagonalization of the configuration interaction Hamiltonian. Spatial symmetries of the exciton states are related to those of the one-particle states by group theory and verified by numerical calculation. It is shown that the lowest exciton state is an optically active A1 exciton. Optical absorption spectra are calculated and compared with available experimental data.

Relationships between complex core level spectra and materials properties

AbstractThe XPS of many oxides are quite complex and there may be several peaks of significant intensity for each subshell. These peaks arise from many‐electron effects, which normally are treated with configuration interaction (CI) wavefunctions where static correlation effects are taken into account. It is common to use semiempirical methods to determine the matrix elements of the CI Hamiltonian and there are few rigorous CI calculations where parameters are not adjusted to fit experiment. In contrast, we present, in the present work, theoretical XPS spectra obtained with rigorous CI wavefunctions for CeO2 where the XPS are especially complex; several different core levels are studied. This study uses an embedded CeO8 cluster model to represent bulk CeO2 and the relativistic CI wavefunctions are determined using four‐component spinors from Dirac‐Fock calculations. In particular, we examine the importance of interatomic many‐body effects where there is a transfer of electrons from occupied oxygen 2p orbitals into empty cation orbitals as it is common to ascribe the complex XPS to this effect. We also contrast the importance of many‐body charge‐transfer effects for the isoelectronic cations of Ce4+ and La3+. The long‐range goal of this work is to relate the XPS features to the nature of the chemical bonding in CeO2 and we describe our progress toward this goal. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Core-valence correlations for atoms with open shells

We present an efficient method of inclusion of the core-valence correlations into the configuration interaction (CI) calculations. These correlations take place in the core area where the potential of external electrons is approximately constant. A constant potential does not change the core electron wave functions and Green's functions. Therefore, all operators describing interaction of $M$ valence electrons and $N-M$ core electrons (the core part of the Hartree-Fock Hamiltonian $V^{N-M}$, the correlation potential $\hat\Sigma_1({\bf r},{\bf r'},E)$ and the screening of interaction between valence electrons by the core electrons $\hat\Sigma_2$) may be calculated with all $M$ valence electrons removed. This allows one to avoid subtraction diagrams which make accurate inclusion of the core-valence correlations for $M>2$ prohibitively complicated. Then the CI Hamiltonian for $M$ valence electrons is calculated using orbitals in complete $V^{N}$ potential (the mean field produced by all electrons); $\hat\Sigma_1$ + $\hat\Sigma_2$ are added to the CI Hamiltonian to account for the core-valence correlations. We calculate $\hat\Sigma_1$ and $\hat\Sigma_2$ using many-body perturbation theory in which dominating classes of diagrams are included in all orders. We use neutral Xe I and all positive ions up to Xe VIII as a testing ground. We found that the core electron density for all these systems is practically the same. Therefore, we use the same $\hat\Sigma_1$ and $\hat\Sigma_2$ to build the CI Hamiltonian in all these systems ($M=1,2,3,4,5,6,7,8$). Good agreement with experiment for energy levels and Land\'{e} factors is demonstrated for all cases from Xe I to Xe VIII.

Solvent Effects, Reaction Coordinates, and Reorganization Energies on Nucleophilic Substitution Reactions in Aqueous Solution

AbstractFor Abstract see ChemInform Abstract in Full Text.

Tools for analysing configuration interaction wavefunctions

The configuration interaction (CI) approach to quantum chemical calculations is a well-established means of calculating accurately the solution to the Schrödinger equation for many-electron systems. It represents the many-body electron wavefunction as a sum of spin-projected Slater determinants of orthogonal one-body spin-orbitals. The CI wavefunction becomes the exact solution of the Schrödinger equation as the length of the expansion becomes infinite, however, it is a difficult quantity to visualise and analyse for many-electron problems. We describe a method for efficiently calculating the spin-averaged one- and two-body reduced density matrices ρ Ψ( r ̄ ; r ̄ ′) and Γ Ψ( r ̄ 1, r ̄ 2; r ̄ ′ 1, r ̄ ′ 2) of an arbitrary CI wavefunction Ψ. These low-dimensional functions are helpful tools for analysing many-body wavefunctions; we illustrate this for the case of the electron–electron cusp. From ρ and Γ one can calculate the matrix elements of any one- or two-body spin-free operator O . For example, if O is an applied electric field, this field can be included into the CI Hamiltonian and polarisation or gating effects may be studied for finite electron systems.

Systematic Study of Selected Diagonalization Methods for Configuration Interaction Matrices

AbstractSeveral modifications to the Davidson algorithm are systematically explored to establish their performance for an assortment of configuration interaction (CI) computations. The combination of a generalized Davidson method, a periodic two‐vector subspace collapse, and a blocked Davidson approach for multiple roots is determined to retain the convergence characteristics of the full subspace method. This approach permits the efficient computation of wave functions for large‐scale CI matrices by eliminating the need to ever store more than three expansion vectors (bi) and associated matrix‐vector products (σi), thereby dramatically reducing the I/O requirements relative to the full subspace scheme. The minimal‐storage, single‐vector method of Olsen is found to be a reasonable alternative for obtaining energies of well‐behaved systems to within μEh accuracy, although it typically requires around 50% more iterations and at times is too inefficient to yield high accuracy (ca. 10−10 Eh) for very large CI problems. Several approximations to the diagonal elements of the CI Hamiltonian matrix are found to allow simple on‐the‐fly computation of the preconditioning matrix, to maintain the spin symmetry of the determinant‐based wave function, and to preserve the convergence characteristics of the diagonalization procedure. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1574–1589, 2001

An Ab Initio Molecular Orbital−Valence Bond (MOVB) Method for Simulating Chemical Reactions in Solution

A mixed molecular orbital and valence bond (MOVB) method for describing the potential energy surface of reactive systems has been developed and applied to a model proton transfer reaction in aqueous solution. The MOVB method is based on a block-localized wave function (BLW) approach for defining the diabatic electronic states. Then, a configuration interaction Hamiltonian is constructed using these diabatic states as the basis function. It was found that the electronic coupling energy is large with a value of about 30 kcal/mol for the H3N−H−NH3+ system, whereas the predicted activation barrier is only 1.2 kcal/mol using the 3-21G basis set. The MOVB results are found to be in good accord with the corresponding ab initio Hartree−Fock calculations for the proton transfer process. We have also incorporated solvent effects into the MOVB Hamiltonian in the spirit of combined QM/MM calculations, and have modeled the proton transfer between ammonium ion and ammonia in water using Monte Carlo simulations. The potential of mean force was computed via free energy perturbation coupled with umbrella sampling techniques using (1) an energy gap mapping approach, and (2) a geometrical mapping procedure. Solvent effects increase the barrier height by about 2.2 kcal/mol from the MOVB and HF ground state potential energy surface. The present study demonstrated the feasibility of ab initio MOVB method for studying chemical reactions by incorporating explicit solvent effects in the description of the reaction coordinate in combined QM/MM simulations.

The effects of triple and quadruple excitations in configuration interaction procedures for the quantum mechanical prediction of molecular properties

The importance of including triple and quadruple excitations (relative to a single Hartree–Fock determinant) in ab initio electronic structure configuration interaction (CI) theory is investigated for several small molecules [HF, N2, CO, H2O, NH3, (3B1) CH2, and (1A1) CH2]. Specifically the effects of these high order electron correlations on equilibrium molecular geometries, dipole moments, harmonic vibrational frequencies, and infrared intensities are reported. Triple and quadruple excitations are generally found to affect the dipole moment, in an absolute sense, only slightly. In some cases, infrared intensities show a medium to large dependence on higher excitations. Molecular geometries, and subsequently the harmonic vibrational frequencies, however, are significantly more dependent upon these higher excitations. Quadruple excitations are found to be significantly more important than triple excitations for all closed shell systems except for CO, where the relative importance of triples to quadruples is roughly 2:3 in predicting for vibrational frequencies. On the other hand, it is found that triples and quadruples are of nearly equal importance for 3B1 CH2. The equilibrium bond length and molecular properties of the multiply bonded species CO and N2 show a larger absolute dependence on the higher than double excitations. Several additional levels of theory [e.g., all singles, doubles, and quadruples (CISDQ)] have been applied to HF and N2 in a more detailed investigation of the structure of the CI Hamiltonian matrix. It is concluded that only a very small subset of the triply and quadruply excited configurations account for nearly all of the higher excitation effects on harmonic frequencies.