Numerically exact configuration interaction at quadrillion-determinant scale

Semiempirical HAM/3 molecular orbital configuration interaction (CI) calculations have been employed to interpret the gas-phase He(I) photoelectron (PE) spectrum of 1,9-dimethylguanine (1,9-DMG). Previous interpretation of the PE spectrum of this molecule, which has a tautomeric structure similar to that of guanine in DNA and RNA, has relied on SCF calculations. Test calculations were performed on pyrimidine. Because HAM/3 calculations without CI were parameterized to describe PE data, ionization potentials (IPS) obtained at the SCF level agree better with experiment than IPS obtained with CI calculations. However, when pyrimidine results from the HAM/3 CI calculations are compared to previously reported results obtained using the outer-valence Green function (OVGF) method or the two-particle-hole Tamm–Dabcoff Green function approximation (2ph-TDA) method, the agreement is satisfactory. The average difference between corresponding values for the first four IPS of pyrimidine obtained from HAM/3 CI, OVGF, and the 2ph-TDA calculations is less than 0.5 eV. Furthermore, for the seven lowest-energy cation states of pyrimidine, the three computational methods yield normalized coefficients associated with the dominant Koopmans configurations that have squares that differ by less than 0.14. For 1,9-DMG, the results of HAM/3 CI calculations indicate that five of the seven lowest-energy ionization events, previously assigned to the first-to-third and to the sixth- and seventh-highest occupied orbitals, are well described within the framework of Koopmans theorem. On the other hand, the fourth and fifth ionization events in 1,9-DMG result in cation states in which there is significant hole-mixing of Koopmans configurations associated with removal of electrons from the second- and third-highest occupied π orbitals. © 1992 John Wiley & Sons, Inc.

GRASP92: a package for large-scale relativistic atomic structure calculations

The configuration interaction (CI) method dates back to the earliest days of quantum mechanics, and is the most straightforward and versatile approach for dealing with electron correlation. The earliest applications typically involved 2–10 terms, while modern molecular CI calculations often employ many millions of configuration state functions (CSFs). In addition to the enormous increase in computer power over the last fifty years, many theoretical developments have contributed to the evolution of the CI approach, including the development of efficient algorithmic tools for the various computational steps and the exploration and optimization of the choices of basis sets, orbitals, and the structure of the CI expansion. Among the milestones in these developments have been the introduction of efficient matrix eigenvalue methods, the introduction of multireference CI expansions, the formulation of various corrections and modifications to overcome the major fault of CI, its lack of extensivity, and particularly the introduction of direct CI, which greatly increased the length of accessible CI expansions by eliminating the need to store the Hamiltonian matrix. Unitary group and related methods have helped make direct CI calculations particularly efficient. Specialized computer programs for full CI calculations have become very efficient and are producing benchmark results which are extremely useful for evaluating other methodologies. Although it has lost ground to the very attractive coupled cluster methods, CI still has an important role to play in quantum chemistry.

X-ray absorption near edge structure (XANES) at L2,3-edge of 3d transition elements is dominated by strong correlation effects among 2p core hole and 3d electrons. In the present study, we have performed systematic configuration interaction (CI) calculations in order to reproduce and interpret Fe-L2,3 XANES of FeO, LaFeO3 and SrFeO3. Relativistic four components wave functions were obtained by solving Dirac equations with density functional theory. CI calculations were made using the relativistic molecular orbitals instead of atomic orbitals, which enables inclusion of the O-2p orbital contributions through covalency. The oscillator strength of the electric dipole transition was then computed. Experimental XANES spectra of three compounds were satisfactorily reproduced by the theoretical spectra obtained for (FeO6)m− clusters in octahedral symmetry. Chemical shifts between compounds were quantitatively reproduced as well. Component analysis of CI was systematically made in order to analyze the origin of differences in spectral shapes.

A computational strategy to analyze Cu-O(2) adducts based on the use of difference-dedicated configuration interaction (DDCI) calculations is presented. The electronic structure, vertical gaps and nature of the metal-O(2) interaction, and the extension of the charge transfer between both fragments have been investigated. Relative stabilities between isomers are determined from triplet states CCSD(T) calculations. The key point of the here proposed strategy rests on the use of a rationally designed active space, containing only those orbitals, which optimize the interaction pathways between LCu and O(2) fragments. The procedure has been tested on a broad set of model and synthetic biomimetic systems, the results compared with previous theoretical evaluations and/or available experimental data. Our study indicates that this strategy can be considered as an alternative approach to multireference second-order perturbation theory methods to deal with this type of systems with remarkable biradical nature.

Experimental photoelectron spectrum of Si2C2- was assigned by ab initio Monte Carlo simulation with the multicanonical/histogram reweighting technique. At first, two structures, linear and ring, were optimized at the MP2/6-31G* level. The multireference configuration interaction (MRCI) calculation reveals that the spectrum cannot be assigned by considering only a single isomer. Also, MRCI calculations cannot explain different widths of the peaks in the spectrum. Multicanonical Monte Carlo simulation with configuration interaction calculation at each step of the simulation was performed for both ring and linear isomers to include the effects of large nuclear motion at finite temperature on the spectrum. It was found that a mixture of two isomers at the experimental condition is necessary to assign the spectrum.

A nonstandard computational scheme has been applied to calculate Fe(CO)(5) with the aim to illustrate the operation of the Dewar-Chatt-Duncanson model by computation. A full configuration interaction (CI) calculation in an active space has been performed. The active space is built from naturally localized molecular orbitals (NLMOs) localized in bond regions or forming lone pairs. For selecting this active space, Weinhold's perturbation theory formulated in the natural bond orbital (NBO) space has been applied. Bonding, lone pair, and antibond NBOs exhibiting large interaction energies serve to define the active space. The actually applied active space, however, comprises NLMOs that are close in shape to the NBOs indicated by perturbation theory. Thus, a CI calculation with localized orbitals has been performed meeting the classical reasoning of chemists that is often based on local bonding concepts. The computational scheme yields the Lewis structure for Fe(CO)(5) whose energy is identical to the Hartree-Fock energy. The Lewis energy comprises CO → Fe σ-electron transfer (ET) and CO ← Fe electron back donation (BD). This Lewis energy gets lowered by localized correlation energy contributions caused by ET processes where electrons are back donated from the Fe d-lone pairs into the CO ligands. Thus, electron correlation within the selected active space is dominated by electron BD. Energies and electron populations of the NBOs support the notion that electrons are preferentially back donated into the equatorial CO ligands. Weights of local Slater determinants, determining the correlation energy, also point to a predominant BD into the equatorial CO ligands. Correlation energy increments resulting from electron BD into single antibond orbitals of the CO ligands have been calculated. These energy quantities also demonstrate that BD into the equatorial CO ligands is more energy lowering than BD into the axial CO ligands.

A method is developed to optimize the separated-pair independent particle (SPIP) wave function; it is a special case of the separated-pair theory obtained by using two-term natural expansions of the geminals. The orbitals are optimized by a theory based on the generalized Brillouin theorem and iterative configuration interaction (CI) calculations in the space of the SPIP function and its single excitations. The geminal expansion coefficients are optimized by serial 2 x 2 CI calculations. Formulas are derived for the matrix elements. An algorithm to implement the method is presented, and the work needed to evaluate the molecular integrals is discussed.

The role played in configuration interaction calculations by the particular form of the orbitals selected as basis is explored by a direct application on the electronic structure of the ground state of the OH molecule. Two configuration interaction studies have been carried out using different sets of one-particle functions: (1) the set natural to the isolated atoms (called AO's) and (2) the orbitals belonging to the molecule (MO's). In (1), using the Hartree-Fock 1s, 2s, and 2p functions for atomic oxygen and the 1s state for hydrogen, and keeping the 1s oxygen state doubly occupied, all Slater determinants of the appropriate ground state symmetry (2π) were found. The dissociation energy and the expansion coefficients of the determinants were determined by a variational procedure which minimized the energy of the system. The nonorthogonality of the basic AO's was treated without approximation by the method of Löwdin. The necessary integrals were calculated on Whirlwind I, the M.I.T. high-speed digital computer; all two-center integrals were computed by expanding the hydrogen orbital about the oxygen center (analogously to the methods of Barnett and Coulson, Coolidge, Löwdin, etc.). In (2), the molecular orbitals (MO's) were found as linear combinations of the above AO's, with coefficients determined by a modified self-consistent field (Roothaan) procedure, in which the energy of a single Slater determinant was made stationary at three values of the internuclear separation. A configuration interaction calculation was then made using these ``best'' MO's as the basic set of one-particle functions. Also included are a calculation of the dipole moment and Mulliken's electron distribution analysis. The results of these studies are discussed and comparison is made to experiment and other theoretical calculations.

Accuracy, variationality, and convergence underpin the reliability of modern electronic structure methods, yet definitive benchmarks in the relativistic regime remain elusive due to the absence of numerically exact full configuration interaction (CI) references. Recent algorithmic advances in the CI framework, enabled by the small-tensor-product (STP) decomposition approach, have dramatically extended the tractable size of the configuration space, making numerically exact CI calculations feasible in large active spaces previously beyond reach. In this work, we employ the recently developed STP-CI framework to perform large-scale numerically exact CI calculations and directly benchmark relativistic coupled cluster and density matrix renormalization group methods. Definitive benchmarking of approximate relativistic electronic structure methods is ensured through the application of the gap theorem, which provides rigorous error bounds on the CI reference and establishes a controlled standard for assessing accuracy, variationality, and convergence.

Using a valence double-zeta polarization basis, full configuration–interaction (FCI) calculations are carried out on water at its equilibrium geometry and at geometries where the OH bond lengths are stretched until dissociation. At the same geometries and with the same basis set configuration interaction calculations at excitation levels up to hextuples, multireference singles doubles configuration interaction calculations, coupled cluster calculations at excitation levels up to quadruples, Mo/ller–Plesset perturbation theory calculations through order fifteen, and complete active space second-order perturbation theory calculations are also carried out. The static correlation contribution increase with increasing bond length. The calculations show that the coupled cluster approach has a remarkable ability to describe even relatively large static correlation contributions. The single reference perturbation expansion breaks down for larger OH bond length, while the multireference approach preserves the accuracy for the whole potential curve. At the equilibrium geometry, FCI calculations have also been carried out for the lowest state of 2A1, 2B1, and 2B2 symmetry of H2O+, and the results compared with state of the art correlation results for total energies and ionization potentials (IP’s). Differential energies (IP’s) are obtained more accurately than absolute (total) energies in the size extensive coupled cluster and perturbation approaches. For the nonsize extensive configuration interaction method errors are obtained of the same size for differential and absolute energies.

Configuration Interaction (CI) calculations are carried out for bond-breaking processes by employing localized molecular orbitals (LMO). It is found that the advantage of this choice relative to the use of canonical orbitals is two-fold: First, the convergence of the truncated CI is speeded up by employing LMO; secondly, since the LMO are localized in certain regions of the molecular system one can divide the LMO in two sets, one which is important for the description of the process under consideration and the other which describes the molecular part not directly involved in the process (“spectator group”). It is found to be sufficient to correlate only the “local active region” of the molecule, and this procedure leads to a much shorter CI expansion without loss of accuracy in describing the chemical process. The CH3 group has been used as “spectator group” and the dissociation into radicals CH3X → CH3 +X and CH3CH2X → CH3CH2+X with X=H, F, NH3+ as well as the charge transfer reaction CH3-X+ → CH3++X and CH3CH2-X+ → CH3CH2++X with X=N2 and NH3 has been studied. For both type of radical reactions the CH3 bonds need not be included in the local active region, while in the charge-transfer process the CH3 can only be considered a spectator group if it is not connected directly to the separating group.

When the one-body part of the relativistic Hamiltonian H is a sum of one-electron Dirac Hamiltonians, relativistic configuration interaction (CI) calculations are carried out with an ad hoc basis of positive-energy orbitals, {uj+, j=1, 2,…,m} and, more recently, with the full bases of positive-energy and negative-energy orbitals, {uj+, uj−, j=1, 2,…,m}. The respective eigenproblems H+Ck+=Ek+Ck+, k=1, 2,…,(m), and HCk=EkCk; k=1, 2,…,(2m) are related through Ek+≤Ek+(2m−(m) [R. Jauregui et al., Phys. Rev. A 55, 1781 (1997)]. This inequality becomes an equality for the independent-particle Hartree–Fock model and some other simple multiconfiguration models, leading to an exact decoupling of positive-energy and negative-energy orbitals. Beyond Hartree–Fock, however, it is generally impossible to achieve an equality. By definition, optimal decoupling is obtained when the difference Ek+(2m)−(m)−Ek+ is a minimum, which amounts to maximize the energy Ek+ with respect to any set of m functions in the 2m-dimensional space {uj+, uj−, j=1, 2,…,m}. Straight maximization is a slowly convergent process. Fortunately, numerical calculations on high-Z atomic states show that optimally decoupled, or best positive-energy orbitals are given, to within 6 decimals in atomic units by the positive-energy natural orbitals of the full eigenfunction Ck+(2m)−(m). Best orbitals can accurately be obtained through CI-by-parts treatments for later use in large-scale relativistic CI, as illustrated with Ne ground-state calculations. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 805–812, 1998

A study is made of the vibrational energy levels and the corresponding oscillation dynamics of the clusters Xe4He2, Xe3He2, and I24He. XeHe2 is a representative of the ‘‘three ball’’ clusters, while I2He is a prototype of the ‘‘stick and ball’’ systems. The treatment is based on the vibrational self-consistent field (SCF) method, which introduces an approximate separation of the modes involved. Success of the method depends on an adequate choice of the coordinates that are being mutually separated. We use physical arguments, based on mass ratios and potential function considerations, as well as comparative SCF calculations in different coordinate systems, to determine the appropriate modes for each system. Numerically exact results are also obtained by configuration interaction (CI) calculations using a basis of SCF states. The SCF and CI calculations include all modes and employ realistic potentials. Several states that are both rotationally and vibrationally excited are also calculated. The main conclusions are: (1) Hyperspherical coordinates are the best modes for XeHe2; ellipsoidal coordinates are best for I2He. In each case, the ‘‘good modes’’ SCF gives energies in remarkable agreement with the exact (CI) ones. (2) XeHe2 resembles a quantum liquid drop: Even in the ground state, it is delocalized over and between the (two) classical equilibrium structures. (3) Structural distributions, rather than rigid geometry, are essential for the description of such floppy clusters. The single-mode SCF wave functions offer a highly accurate description of the structural distributions. (4) There is a sequence of bound, excited rotational states of I2He in which the He precesses around the I2 axis. The amplitude of the I2He bending vibrations are very large (θA<20°), but none of the bound states involves a full rotational motion around the I2 stick (with angular momentum normal to the axis). The SCF method with the ‘‘good coordinates’’ proposed here is expected to yield results of similar high accuracy for any cluster of the ‘‘three balls’’ or ‘‘stick and ball’’ types.

The electronic structure of the lead monofluoride molecule is studied by means of ab initio configuration interaction (CI) calculations including the spin-orbit interaction. Potential-energy curves are generated for a large number of electronic states, of which only the X1 2Π1/2 ground and X2 2Π3/2 and A 2Σ+ excited states have been observed experimentally. Two different methods are compared for the inclusion of spin-orbit effects in the theoretical treatment, a contracted CI which employs a basis of large-scale Λ–S eigenfunctions to form a rather small matrix representation of the full relativistic Hamiltonian (two-step approach), and a more computationally laborious technique which involves solution of a secular equation of order 250 000 S2 eigenfunctions of different spin and spatial symmetry to achieve a potentially more evenly balanced description of both relativistic and electron correlation effects (one-step approach). In the present application, it is found that both methods achieve quite good agreement with measured spectroscopic constants for the X1, X2, and A states. The simpler of these methods is also employed to predict the radiative lifetimes of the latter two states. The key A 2Σ+–X 2Π transition moment in these calculations is found to vary strongly with internuclear distance and to vanish in the neighborhood of the respective equilibrium distances of both participating states. The computed lifetime for the A, v′=0 state of 16 μs overestimates the corresponding measured value by a factor of three, but those of higher vibrational states are found to decrease rather sharply with increasing v′, suggesting that only a slight displacement of the theoretical A–X transition moment curve is needed to explain the above discrepancy.