Configuration Interaction Values Research Articles

Calculating energy derivatives for quantum chemistry on a quantum computer

Modeling chemical reactions and complicated molecular systems has been proposed as the “killer application” of a future quantum computer. Accurate calculations of derivatives of molecular eigenenergies are essential toward this end, allowing for geometry optimization, transition state searches, predictions of the response to an applied electric or magnetic field, and molecular dynamics simulations. In this work, we survey methods to calculate energy derivatives, and present two new methods: one based on quantum phase estimation, the other on a low-order response approximation. We calculate asymptotic error bounds and approximate computational scalings for the methods presented. Implementing these methods, we perform geometry optimization on an experimental quantum processor, estimating the equilibrium bond length of the dihydrogen molecule to within 0.014 Å of the full configuration interaction value. Within the same experiment, we estimate the polarizability of the H{}_{2} molecule, finding agreement at the equilibrium bond length to within 0.06 a.u. (2 % relative error).

Machine Learning Configuration Interaction for ab Initio Potential Energy Curves.

The concept of machine learning configuration interaction (MLCI) (J. Chem. Theory Comput. 2018, 14, 5739), where an artificial neural network (ANN) learns on the fly to select important configurations, is further developed so that accurate ab initio potential energy curves can be efficiently calculated. This development includes employing the artificial neural network also as a hash function for the efficient deletion of duplicates on the fly so that the single and double space does not need to be stored and this barrier to scalability is removed. In addition, configuration state functions are introduced into the approach so that pure spin states are guaranteed, and the transferability of data between geometries is exploited. This improved approach is demonstrated on potential energy curves for the nitrogen molecule, water, and carbon monoxide. The results are compared with full configuration interaction values, when available, and different transfer protocols are investigated. It is shown that, for all of the considered systems, accurate potential energy curves can now be efficiently computed with MLCI. For the potential curves of N2 and CO, MLCI can achieve lower errors than stochastically selecting configurations while also using substantially less processor hours.

Interplay between Electronic Correlation and Metal-Ligand Delocalization in the Spectroscopy of Transition Metal Compounds: Case Study on a Series of Planar Cu2+ Complexes.

We present a comprehensive theoretical study of the physical phenomena that determine the relative energies of three of the lowest electronic states of each of the square-planar copper complexes [CuCl4]2-, [Cu(NH3)4]2+, and [Cu(H2O)4]2+ and present a detailed analysis of the extent to which truncated configuration interaction (CI) and coupled cluster (CC) theories succeed in predicing the excitation energies. We find that ligand-metal charge transfer (CT) single excitations play a crucial role in the correct determination of the properties of these systems, even though the first impact of these CT on the energetics of these systems appears at fourth-order in perturbation theory. We provide a minimal selected CI space for describing these systems with multireference theories and use a high-order perturbation theory analysis within this space to derive a simple and general physical picture for the LMCT process. We find that coupled cluster singles and doubles (CCSD) energy differences agree very well with near full CI values even though the D1 diagnostics are large, which casts doubt on the usefulness of single-amplitude-based multireference diagnostics. Configuration interaction singles and doubles (CISD) severely underestimates the excitation energies, and the failure is a direct consequence of the size-inconsisency errors in CISD. Finally, we present reference values for the energy differences computed using explicitly correlated CCSD(T) and BCCD(T) theory.

Unitary coupled-cluster based self-consistent polarization propagator theory: A third-order formulation and pilot applications.

In this article, the development of a third-order self-consistent polarization propagator method based on unitary coupled-cluster (UCC) parametrization of the ground-state wavefunction and the excitation manifold comprising unitary-transformed excitation operators, hereafter referred to as UCC3, is reported. The UCC3 method is designed to provide excitation energies correct up to the third order for excited states dominated by single excitations. An expansion for the UCC transformed Hamiltonian involving Bernoulli numbers as expansion coefficients is adopted in the derivation of UCC3 working equations. Interestingly, UCC-based polarization propagator theory offers an alternative derivation for the strict version of the third-order algebraic diagrammatic construction [ADC(3)-s] method. The UCC3 results for the excitation energies of excited states in H2O, HF, N2, Ne, CH2, BH, and C2 molecules are compared with benchmark full configuration interaction values as well as ADC(3) and equation-of-motion coupled-cluster singles and doubles results to demonstrate the accuracy of the UCC3 method. UCC-based self-consistent polarization propagator theory appears to be a promising framework for developing non-perturbative hermitian formulations for treating electronically excited states.

On the HCN - HNC Energy Difference.

The value for the HCN → HNC 0 K isomerization energy has been investigated by combining state-of-the-art electronic structure methods with the Active Thermochemical Tables (ATcT) approach. The directly computed energy difference between HCN and HNC at the HEAT-456QP level of theory is 5236 ± 50 cm(-1). This is substantially lower (by ∼470 cm(-1) or ∼1.3 kcal/mol) than the recently proposed high-level multireference configuration interaction value of 5705 ± 20 cm(-1) of Barber et al. ( Mon. Not. R. Astron. Soc. 2014, 437, 1828-1835 ). The discrepancy was analyzed by the ATcT approach, using several distinct steps, which (a) independently corroborated the current single-reference HEAT-456QP result, (b) independently found that the recent multireference-based value is highly unlikely to be correct within its originally stated uncertainty, and (c) produced a recommended value of 5212 ± 30 cm(-1) for the HCN → HNC isomerization energy at 0 K, based on all currently available knowledge. The ATcT standard enthalpies of formation at 0 and 298 K for HCN, HNC, and their cations and anions are also presented.

Application of state-specific multireference Møller–Plesset perturbation theory to nonsinglet states

We present molecular applications of a spin free size-extensive state-specific multireference perturbation theory (SS-MRPT), which is valid for model functions of arbitrary spin and generality. In addition to the singlet states, this method is equally capable to handle nonsinglet states. The formulation based on Rayleigh-Schrodinger approach works with a complete active space and treats each of the model space functions democratically. The method is capable of handling varying degrees of quasidegeneracy and of ensuring size consistency as a consequence of size extensivity. In this paper, we illustrate the effectiveness of the Møller-Plesset (MP) partitioning based spin free SS-MRPT [termed as SS-MRPT(MP)] in computations of energetics of the nonsinglet states of several chemically interesting and demanding molecular examples such as LiH, NH(2), and CH(3). The spectroscopic constants of (3)Sigma(-) state of NH and OH(+) molecular systems and the ground (1)Sigma(g) (+) as well as excited (3)Sigma(u)(+) states of N(2) have been investigated and comparison with experimental and full configuration interaction values (wherever available) has also been provided. We have been able to demonstrate here that the SS-MRPT(MP) method is an intrinsically consistent and promising approach to compute reliable energies of nonsinglet states over different geometries.

Polarizability of theSi2+ion

The dipole polarizability of the ${\mathrm{Si}}^{2+}$ ground state has been determined by a large-scale configuration-interaction (CI) calculation using the sum-over-states approach. The CI calculation was used to describe the valence electron dynamics with respect to the Hamiltonian which treats core-valence correlations with a semiempirical approach. Various higher-order polarizabilies were computed, and this permitted a more refined analysis of the energy intervals measured by resonant excitation Stark ionization spectroscopy (RESIS). The polarizability derived from the revised analysis of the RESIS data was $11.669(9)\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$, only 0.03% larger than that reported in Komara et al. [J. Phys. B 38, 87 (2005)]. The CI value of the polarizability, $11.688\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$, was only 0.2% larger than experiment, while the quadrupole polarizability of $35.75\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ was also consistent with experiment. A resonant oscillator strength of 1.621(3) was derived from the experimental dipole polarizability.

Hole-particle characterization of coupled-cluster singles and doubles and related models

The hole-particle analysis introduced in the paper [J. Chem. Phys. 124, 224109 (2006)] is fully described and extended for coupled-cluster models of practical importance. Based on operator renormalization of the conventional amplitudes t(ai) and t(ab,ij), we present a simplified method for estimating the hole-particle density matrices for coupled-cluster singles and doubles (CCSD). With this procedure we convert the first-order density matrix of the configuration interaction (CI) singles and doubles (CISD) model, which lacks size consistency, into an approximately size-consistent expression. This permits us to correctly estimate specific indices for CCSD, including the hole and particle occupation numbers for each atom, the total occupation of holes/particles, and the entropylike measure for effective unpaired geminals. Our calculations for simple diatomic and triatomic systems indicate reasonable agreement with the full CI values. For CCSD and CISD we derive special types of two-center indices, which are similar to the charge transfer analysis of excited states previously given within the CIS model. These new quantities, termed charge transfer correlation indices, reveal the concealed effects of atomic influence on electronic redistribution due to electron correlation.

Theoretical studies of isotope shifts, hyperfine structures and oscillator strengths in transitions between low-lying levels in O I

Multiconfiguration Hartree-Fock (MCHF) and configuration interaction (CI) calculations have been performed for the low-lying levels 2p4 3P, 2p3(4S0)3s 3,5S0 and 2p3(4S0)3p 3,5P0 of neutral oxygen. Different cancellation effects on the specific mass shift, on the electronic contributions to hyperfine interaction constants and on the length and velocity forms of oscillator strengths are illustrated. The final CI values are compared with experimental values and, when available, with values from other theories.

Comparison between explicitly correlated and density functional theory calculations in mixed-valence model systems

Considering simple model problems, symmetric mixed-valence compounds are studied by both accurate ab initio configuration interaction (CI) and standard (B3LYP) density functional theory (DFT) calculations. The DFT estimates of the effective hopping integral t for mixed-valence compounds are generally smaller (by 20%) than the CI values, in contrast to those of the exchange coupling constant in magnetic systems which are usually overestimated. Qualitatively divergent behaviors of DFT versus CI results have been found in some cases. Possible origins of these discrepancies are discussed.

A CSF-based multi-reference coupled pair approximation

Using the newly developed multi-reference coupled pair approximation program code, the adiabatic potential curves of the ground states of F2, As2 and As2+ were calculated. Computed spectroscopic constants of these molecules were found to be in good agreement with experimental values. The resulting binding energy of As2 (3.86 eV) was compared with the experimental value of 3.99 eV [15] and the best multi-reference configuration interaction value (3.58 eV) reported previously by the present authors. The calculated first adiabatic ionization potential of As2 (9.67 eV) was found to be in good agreement with the experimental result.

Effect of different subsets on convergence patterns of hyperspherical harmonic expansion for theS states of the helium atom

Effects of different subsets on convergence patterns of hyperspherical harmonic (HH) expansions for the low-lying 1S and 3S states of the helium atom have been investigated with the correlation-function-hyperspherical-harmonic-generalized-Laguerre-function (CFHHGLF) method by successively introducing HH subsets with the fixed three-dimensional angular momentums (l) into the atomic wave functions. The eigenenergies given by the HH subsets of l=0, 1, 2, and 3 are in good agreement with the best s-, sp-, spd-, and spdf limits of variational configuration interaction (CI) calculations, respectively. The final eigenenergies of the ground state as well as the examined low-lying excited 1S and 3S states are quite close to the exact Hylleraas CI (HCI) values at the sixth decimal place. Moreover, l=0 and l≠0 expansion results also tell us that it is not necessary to take into account too many HHs at the given l, especially for higher l, and that the more the absolute electron correlation energies the bigger l it takes to obtain precise eigenenergies. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 661–668, 1997

Calculation of excitation and photoionization spectra by quasi‐degenerate perturbation theory

AbstractThe ability of the QDPT CI method, in which the quasi‐degenerate perturbation theory is applied within the configuration interaction (CI) approach, in dealing with the calculation of excitation and photoionization spectra is shown through an overview of comparisons between the QDPT CI values and the full CI ones in the same basis set. A direct comparison with the experimental data is given for the core photoelectron spectrum of Ne and the valence photoelectron spectra of Ar and HCl. The quality of the results obtained is very satisfactory, both as regards the energies and the wave functions, indicating the validity and the flexibility of the method that can confidently be applied also in cases where strong correlation effects are present. © 1994 John Wiley & Sons, Inc.

Ground‐state correlation energy of Ne

AbstractA series of basis sets and configuration interaction (CI) wave functions, both of which were constructed so as to systematically approach to the complete set limit and the full CI limit, were used for the ground state of Ne. These calculations yielded an estimated correlation energy of −0.3891 au, which is 99.6% of a recent theoretical estimate of −0.3905 au. The CI value, −0.3821 au, was obtained by SDCI calculation with seven reference configurations by using Slater‐type orbitals (STOs) from s to h functions. © 1994 John Wiley & Sons, Inc.

A comparison of unrestricted Hartree–Fock- and restricted open-shell Hartree–Fock-based methods for determining the magnetic hyperfine parameters of NO (X 2Π)

The magnetic hyperfine structure parameters of NO X 2Π have been determined through a variety of ab initio methods based on restricted and unrestricted Hartree–Fock zeroth order wave functions. Examples of the former include singles configuration interaction (CI), multireference CI, and averaged coupled pair functional theory. Examples of the latter include Mo/ller–Plesset perturbation theory (through fifth order, with estimates to infinite order), coupled cluster methods, and quadratic CI (with approximate inclusion of triple and quadruple excitations). The performance of the various methods in reproducing the difficult-to-describe 14N and 17O isotropic hyperfine interactions is judged in light of both experimental data, where available, and estimated full CI values. The full CI limit was approached through a systematic sequence of ever-more-extensive, selected multireference CI wave functions that would, in principle, include the full CI as its final element. While the isotropic coupling constants were found to converge very slowly along this sequence, at least in comparison to other one-electron properties, the selected CI approach was efficient enough in its recovery of correlation effects to be used with large basis sets. The biggest calculation in the sequence of CI wave functions included over two million configurations. Energies and properties exhibited sufficient regularity to allow fitting with simple functional forms. The error arising from the lack of basis set completeness is estimated by comparison to fully numerical, partial-wave self-consistent field (SCF) and singles CI results. Effects due to vibrational motion are accounted for by numerical integration of the one-dimensional Schrödinger equation.

Calculation of excitation energies using quasidegenerate variational perturbation theory and multireference-averaged coupled-pair functional theory

Results are presented for the ground and excited states of Be and SiH 2 from ab initio multireference singles and doubles configuration interaction, quasidegenerate variational perturbation theory, and multireference-averaged coupled-pair functional theory calculations. The results are compared with previously obtained full configuration interaction studies. It is seen that quasidegenerate variational perturbation theory and multireference-averaged coupled-pair functional theory yield accurate total energies and excitation energies, even for states that are not the lowest in a given symmetry. Increased accuracy is obtained for excitation energies as the reference space is expanded. In these systems we find that for a fixed small reference space, multireference-averaged coupled-pair functional theory yields total energies closer to full configuration interaction values than either quasidegenerate variational perturbation theory or multireference singles and doubles configuration interaction. As the reference space size is increased averaged coupled-pair functional theory and configuration interaction yield comparable errors in the total energy. Comparison is also made with Davidson-corrected multireference singles and doubles configuration interaction results. Similar results to those given by quasidegenerate variational perturbation theory were obtained.

Isotropic coupling constant for the nitrogen atom from correlated calculations based on spin-unrestricted wave functions

The isotropic hyperfine coupling constant for the ground electronic state of the nitrogen atom is computed from the quadratic configuration interaction correlation procedure based on a single unrestricted Hartree–Fock (UHF) determinant. The splitting is determined from the normalized spin density at the nucleus, derived by finite-field perturbation theory. Results obtained are compared with previous work based on spin-restricted reference spaces. Close accord is found between present estimates and full configuration interaction values for small basis sets. Contributions from shells of higher angular momentum functions in the basis set are similar in both approaches and for the largest unrestricted calculation the correlated results are in good accord with experiment. The UHF wave function is shown to provide a reasonable account of the K-shell contribution to the isotropic coupling and hence the UHF-based correlated calculations show much less sensitivity to the neglect of core–electron correlation than the dramatic effects observed in spin-restricted treatments.

Ab Initio CI Calculations of the Energy Difference between Trimethylenemethane and Butadiene

AbstractAb initio configuration interaction (CI) calculations have been carried out in order to determine the energy difference between 3A î2 trimethylenemethane (TMM) and 1Ag butadiene. The pi CI value of 38.3 kcal/mol is very similar to the CI values obtained when excitations of the sigma electrons are permitted. This finding suggests that correlation effects involving sigma orbitals make at most a small contribution to the energy differences between non‐Kekulé hydrocarbon diradicals and their closed‐shell isomers. Possible complications in the experimental measurement of this energy difference are discussed. It is pointed out that methylenecyclopropane might be formed in attempts to deprotonate the 2‐methallyl cation, without the involvement of TMM. From the experimental heats of formation of methylenecyclopropane and butadiene, an energy difference of 14–16 kcal/mol between 3A î2 TMM and methylenecyclopropane is estimated. This is in excellent agreement with a previous energy difference obtained by direct calculation.

Oscillator strengths of the transition 3p63d2D→3p53d22P0in the potassium isoelectronic sequence

The excitation threshold and oscillator strengths for the 3p63d2D to 3p53d2 2P0 transition in Sc2+, Ti3+ and V4+ ions of the potassium sequence have been calculated using both Hartree-Fock (HF) and configuration interaction (CI) wavefunctions. For Ti3+, the HF length value of the oscillator strength (fl) is close to the recent value of Griffin et al. (1982), although for all three ions, the HF velocity value (fv) is only about half the length value. The CI values of fl and fv are in much closer agreement with each other, but differ substantially from the HF values. This demonstrates the importance of including CI for these transitions. The authors predict the positions of the multiplets 3p53d2(1D)2P0 and 3p53d2(1S)2P0 in V4+ to be 317500 cm-1 and 376000 cm-1, respectively, above the ground state.

Reduced Partitioning Procedure in Configuration Interaction Studies. I. Ground States

A variation-perturbation approach to configuration interaction (CI) studies of atoms and molecules has been derived which yields a series of converging upper bounds to the CI energy. As a consequence, the method permits an adequate representation of a large n-particle wavefunction in terms of a very low order nonlinear perturbation summation. This ``reduction'' procedure is found to have simplifications for full CI studies as well as suggesting certain systematic improvements over the standard Hartree-Fock (HF) and ``truncated'' CI calculations. The first order solution, which is equivalent to the application of a geometric sumrule to the perturbation expansion is also shown to be derivable from a ``steepest descent'' argument. In preliminary calculations on H2 and the HeH+ molecular ion with a HF function as the unperturbed state, the first order result gives 60% to 70% of the energy difference between the full CI energy and the HF value, while only a third order treatment accounts for better than 90%. Potential curves for the ground state of HeH+ for the eight lowest orders of solution and their spectroscopic parameters are also obtained, with the eighth order energies differing from the full CI values by less than 10−4 a.u. at all internuclear separations.