Configuration Interaction Wavefunctions Research Articles

Coupled Cluster Externally Corrected by Adaptive Configuration Interaction.

An externally corrected coupled cluster (CC) method, where an adaptive configuration interaction (ACI) wave function provides the external cluster amplitudes, named ACI-CC, is presented. By exploiting the connection between configuration interaction and CC through cluster analysis, the higher-order T3 and T4 terms obtained from ACI are used to augment the T1 and T2 amplitude equations from traditional CC. These higher-order contributions are kept frozen during the CC iterations and do not contribute to an increased cost with respect to coupled cluster including the single and double excitations (CCSD). We have benchmarked this method on three closed-shell systems: beryllium dimer, carbonyl oxide, and cyclobutadiene, with good results compared to other corrected CC methods. In all cases, the inclusion of these external corrections improved upon the "gold standard" CCSD(T) results, indicating that ACI-CCSD(T) can be used to assess strong correlation effects in a system and as an inexpensive starting point for more complex external corrections.

Calculating the distance from an electronic wave function to the manifold of Slater determinants through the geometry of Grassmannians

The set of all electronic states that can be expressed as a single Slater determinant forms a submanifold, isomorphic to the Grassmannian, of the projective Hilbert space of wave functions. We explored this fact by using tools of Riemannian geometry of Grassmannians as described by Absil et. al [Acta App. Math. 80, 199 (2004)], to propose an algorithm that converges to a Slater determinant that is critical point of the overlap function with a correlated wave function. This algorithm can be applied to quantify the entanglement or correlation of a wave function. We show that this algorithm is equivalent to the Newton method using the standard parametrization of Slater determinants by orbital rotations, but it can be more efficiently implemented because the orbital basis used to express the correlated wave function is kept fixed throughout the iterations. We present the equations of this method for a general configuration interaction wave function and for a wave function with up to double excitations over a reference determinant. Applications of this algorithm to selected electronic systems are also presented and discussed.

Portably parallel construction of a configuration-interaction wave function from a matrix-product state using the Charm++ framework.

The construction of configuration-interaction (CI) expansions from a matrix product state (MPS) involves numerous matrix operations and the skillful sampling of important configurations in a large Hilbert space. In this work, we present an efficient procedure for constructing CI expansions from MPS employing the parallel object-oriented Charm++ programming framework, upon which automatic load-balancing and object migrating facilities can be employed. This procedure was employed in the MPS-to-CI utility (Moritz et al., J. Chem. Phys. 2007, 126, 224109), the sampling-reconstructed complete active-space algorithm (SR-CAS, Boguslawski et al., J. Chem. Phys. 2011, 134, 224101), and the entanglement-driven genetic algorithm (EDGA, Luo et al., J. Chem. Theory Comput. 2017, 13, 4699). It enhances productivity and allows the sampling programs to evolve to their population-expansion versions, for example, EDGA with population expansion (PE-EDGA). Further, examples of 1,2-dioxetanone and firefly dioxetanone anion (FDO- ) molecules demonstrated the following: (a) parallel efficiencies can be persistently improved by simply by increasing the proportions of the asynchronous executions and (b) a sampled CAS-type CI wave function of a bi-radical-state FDO- molecule utilizing the full valence (30e,26o) active space can be constructed within a few hours with using thousands of cores.

Exploring Hilbert space on a budget: Novel benchmark set and performance metric for testing electronic structure methods in the regime of strong correlation.

This work explores the ability of classical electronic structure methods to efficiently represent (compress) the information content of full configuration interaction (FCI) wave functions. We introduce a benchmark set of four hydrogen model systems of different dimensionalities and distinctive electronic structures: a 1D chain, a 1D ring, a 2D triangular lattice, and a 3D close-packed pyramid. To assess the ability of a computational method to produce accurate and compact wave functions, we introduce the accuracy volume, a metric that measures the number of variational parameters necessary to achieve a target energy error. Using this metric and the hydrogen models, we examine the performance of three classical deterministic methods: (i) selected configuration interaction (sCI) realized both via an a posteriori (ap-sCI) and variational selection of the most important determinants, (ii) an a posteriori singular value decomposition (SVD) of the FCI tensor (SVD-FCI), and (iii) the matrix product state representation obtained via the density matrix renormalization group (DMRG). We find that the DMRG generally gives the most efficient wave function representation for all systems, particularly in the 1D chain with a localized basis. For the 2D and 3D systems, all methods (except DMRG) perform best with a delocalized basis, and the efficiency of sCI and SVD-FCI is closer to that of DMRG. For larger analogs of the models, the DMRG consistently requires the fewest parameters but still scales exponentially in 2D and 3D systems, and the performance of SVD-FCI is essentially equivalent to that of ap-sCI.

Distribution of oscillator strengths and correlated electron dynamics in artificial atoms

The electronic structure of the quasi-two-dimensional disk-like artificial atom involving holes inside has been studied by the full configuration interaction (FCI) wave function employing mixed basis sets consisting of standard atomic orbitals and anisotropic Gaussian-type functions. The one-particle confinement potential for electrons has been modeled by a sum of an anisotropic harmonic-oscillator potential and attractive Coulomb potentials, the latter being responsible for the hole positive charges. The oscillator strengths from the ground state to a number of low-lying excited states have been calculated by the FCI energies and wave functions for different strength of the harmonic confinement ω. The results for two electrons with a hole at the center, namely, the He-like system, have shown accumulation of the oscillator strengths distributed among different dipole-allowed transitions in the excitation into the center-of-mass modes or the plasmon modes for increasing confinement strength ω. The system of two electrons with two impurity holes, namely, the H2-like system, has been also studied, which has shown a far more complicated trend of the oscillator strengths with respect to ω owing to the additional degree of freedom of the internuclear distance r. The observed trend has been rationalized on the basis of the nodal patterns in the molecular orbitals and in the electron density distributions.

Incorporating dynamic correlation into the variational determination method of the second‐order reduced density matrix in the doubly occupied configuration interaction space

AbstractThe variational determination of the second‐order reduced density matrices arising from N‐electron doubly occupied configuration interaction wave functions has recently been proposed as a method to describe systems possessing static correlation in their ground states. In this work, we propose to combine this approach with the on‐top pair density functional theory in order to incorporate dynamic correlations and improve the description of systems possessing both types of electron correlation. The procedure requires ensuring that the second‐order reduced density matrix elements satisfy determined N‐representability variational conditions, as well as other constraints arising from the doubly‐occupied configuration interaction wave function features. An analysis of the results obtained through this method, in studies of strongly correlated many‐electron systems, shows the usefulness of our proposals.

Magnetic exchange interactions in monolayer CrI3 from many-body wavefunction calculations

The marked interplay between the crystalline, electronic, and magnetic structure of atomically thin magnets has been regarded as the key feature for designing next-generation magneto-optoelectronic devices. In this respect, a detailed understanding of the microscopic interactions underlying the magnetic response of these crystals is of primary importance. Here, we combine model Hamiltonians with multireference configuration interaction wavefunctions to accurately determine the strength of the spin couplings in the prototypical single-layer magnet CrI3. Our calculations identify the (ferromagnetic) Heisenberg exchange interaction J = −1.44 meV as the dominant term, being the inter-site magnetic anisotropies substantially weaker. We also find that single-layer CrI3 features an out-of-plane easy axis ensuing from a single-ion anisotropy A = −0.10 meV, and predict g-tensor in-plane components and out-of-plane component g zz = 1.92. In addition, we assess the performance of a dozen widely used density functionals against our accurate correlated wavefunctions calculations and available experimental data, thereby establishing reference results for future first-principles investigations. Overall, our findings offer a firm theoretical ground to recent experimental observations.

Quantifying Multireference Character in Multicomponent Systems with Heat-Bath Configuration Interaction

Multicomponent quantum chemical methods seek to include nuclear quantum effects of select nuclei in quantum chemistry calculations by not invoking the Born-Oppenheimer approximation for these nuclei. In multicomponent methods, the inclusion of electron-proton correlation is essential for obtaining even qualitatively accurate protonic densities. However, most of the recently developed multicomponent methods have either used or obtained molecular orbitals from a single-reference mean-field wave function that neglects all electron-proton correlation that is analogous to using Hartree-Fock orbitals in a single-component framework. We examine the consequences of using Hartree-Fock orbitals in multicomponent calculations by developing the multicomponent heat-bath configuration interaction (HCI) method. Multicomponent HCI is a multicomponent selected configuration interaction (CI) technique that enables an accurate approximation of a complete active space or truncated CI wave function for systems with large active spaces. The multicomponent HCI method is shown to reproduce the ground-state protonic density of the HeHHe+, HCN, and FHF- systems when compared to reference grid-based calculations. For all three systems, the coefficient of the leading configuration in the wave function expansion is less than 0.95, indicating that all systems have multireference character. This is highly noteworthy as none of the systems have multireference character in a single-component framework and suggests that multireference character appears inherent to or at least more commonly in a multicomponent framework than a single-component framework. Even when natural orbitals are used rather than Hartree-Fock orbitals for the multicomponent HCI calculations, aspects of the multireference character remain for FHF- and HCN. Consequences and implications of the multireference character of multicomponent quantum chemical systems are discussed.

On the nonadiabatic collisional quenching of OH(A) by H2: a four coupled quasi-diabatic state description.

A four-state diabatic potential energy matrix (DPEM), Hd, for the description of the nonadiabatic quenching of OH(A2Σ+) by collisions with H2 is reported. The DPEM is constructed as a fit to adiabatic energies, energy gradients, and derivative couplings obtained exclusively from multireference configuration interaction wave functions. A four-adiabatic-electronic-state representation is used in order to describe all energetically accessible regions of the nuclear coordinate space. Partial permutation-inversion symmetry is incorporated into the representation. The fit is based on electronic structure data at 42 882 points, described by over 1.6 million least squares equations with a root mean square (mean unsigned) error of 178(83) cm-1. Comparison of ab initio and Hd determined minima, saddle points, and energy minimized points on C2v, Cs, C∞v, and C1 (noncoplanar) portions of two conical intersection seams are used to establish the accuracy of the Hd.

An adiabatic connection for doubly-occupied configuration interaction wave functions.

An adiabatic connection (AC) is developed as an electron correlation correction for doubly occupied configuration interaction (DOCI) wave functions. Following the work of Pernal [Phys. Rev. Lett. 120, 013001 (2018)], the working equations of the approach, termed AC-DOCI, are rooted in the extended random phase approximation (ERPA) and require knowledge of only the ground-state two-electron reduced density matrix (2RDM) from the DOCI. As such, the AC is naturally suited to modeling electron correlation in variational 2RDM (v2RDM)-based approximations to the DOCI. The v2RDM-driven AC-DOCI is applied to the dissociation of molecular nitrogen and the double dissociation of water; the approach yields energies that are similar in quality to those from second-order multireference perturbation theory near equilibrium, but the quality of the AC-DOCI energy degrades at stretched geometries. The exact adiabatic connection path suggests the assumption that the one-electron reduced-density matrix is constant along the AC path is invalid at stretched geometries, but this deficiency alone cannot explain the observed behavior. Rather, it appears that the ERPA's single-particle-transition ansatz cannot, in general, provide good approximations to the 2RDM along the AC path. The AC-DOCI is also applied to a set of 45 reaction energies; for these systems, the approach has an average accuracy that is comparable to that of single-reference second-order many-body perturbation theory.

Analytic non-adiabatic derivative coupling terms for spin-orbit MRCI wavefunctions. II. Derivative coupling terms and coupling angle for KHeA2Π1/2⇔KHeB2Σ1/2.

A method for calculating the analytic nonadiabatic derivative coupling terms (DCTs) for spin-orbit multi-reference configuration interaction wavefunctions is reviewed. The results of a sample calculation using a Stuttgart basis for KHe are presented. Additionally, the DCTs are compared with a simple calculation based on the Nikitin's 3 × 3 description of the coupling between the Σ and Π surfaces, as well as a method based on Werner's analysis of configuration interaction coefficients. The nonadiabatic coupling angle calculated by integrating the radial analytic DCTs using these different techniques matches extremely well. The resultant nonadiabatic energy surfaces for KHe are presented.

A systematic construction of configuration interaction wavefunctions in the complete CI space.

We introduce a systematic approach to construct configuration interaction (CI) wavefunctions through a variant of the Monte Carlo CI (MCCI) method termed systematic-MCCI. Within this approach, the entire interacting space is systematically considered in batches, with the most important configurations across all batches becoming potential additions to the wavefunction. We compare this method to MCCI and a novel pruned-full configuration interaction (FCI) approach. For the ground state of neon, as described by the cc-pVTZ basis, we observe no apparent difference between systematic-MCCI, pruned-MCCI, and MCCI, with all recovering 99% of the correlation energy and producing a very similar wavefunction composition. We then consider the potential energy surface corresponding to the symmetric double hydrogen dissociation of water within a cc-pVDZ basis. Once again MCCI performs comparably to the systematic approaches. Despite systematic-MCCI having longer run times across the number of processors considered, we do observe very good scalability. We then extend this comparison to the first A1 excited energy of carbon monoxide using the cc-pVDZ basis where the MCCI methods perform similarly, approximating this aforementioned energy to within 0.1 eV despite vast reduction in the wavefunction size. Finally, we consider the chromium dimer with the cc-pVTZ basis and 18 frozen orbitals. Here, we find that the systematic approach avoids being trapped in the same local minimum of configuration space as MCCI, yet MCCI can reach a lower energy by repeating the calculation with more processors.

Stochastic perturbation theory in a limited configuration space.

A general-order stochastic perturbation algorithm is obtained from the order-by-order expansion of the imaginary-time evolution of a configuration interaction wave function. A truncation of configuration space that is required for the practical treatment of the perturbative corrections, however, does not preserve size-consistency as is the case for a truncated configuration interaction. To circumvent this problem, we formulate a linked variant of stochastic perturbation theory based on the coupled-cluster ansatz. The implementation based on the linearized coupled-cluster is compared with several full configuration interaction results. We also compare the results with those obtained from deterministic coupled-cluster and many-body perturbation theories.

Revisiting electron-correlation effects on valence shake-up satellites of neon

We report an electron momentum spectroscopy study on valence shake-up satellites of neon. A symmetric noncoplanar $(e,2e)$ experiment was performed at an incident electron energy of 1.2 keV, and the recoil-ion-momentum--dependent $(e,2e)$ cross sections or momentum profiles of the shake-up satellites have been obtained. Furthermore, theoretical momentum profiles have been calculated on the basis of the distorted-wave Born approximation using configuration interaction wave functions of the initial neutral and final ionic states. Comparison between experiment and theory has revealed that contrary to a general expectation, electron correlation in the initial neutral state has a significant influence on the shapes of momentum profiles for neon satellites. It has been shown that the Dyson orbitals of transitions to the $2{p}^{4}(^{1}\mathrm{S})3s\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{S}$ and $2{p}^{4}(^{1}\mathrm{D})3p\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{P}$ ionic states are more localized than those of the associated primary ionizations due to electron-correlation effects.

Potential Energy Curves for Formation of the CH2O2 Criegee Intermediate on the 3CH2 + 3O2 Singlet and Triplet Potential Energy Surfaces.

The potential energy curves (PECs) for the interaction of 3CH2 with 3O2 in singlet and triplet potential energy surfaces (PESs) leading to singlet and triplet Criegee intermediates (CH2OO) are studied using electronic structure calculations. The bonding mechanism is interpreted by analyzing the ground state multireference configuration interaction (MRCI) wave function of the reacting species and at all points along the PES. The interaction of 3CH2 with 3O2 on the singlet surface leads to a flat long-range attractive PEC lacking any maxima or minima along the curve. The triplet surface stems into a maximum along the curve resulting in a transition state with an energy barrier of 5.3 kcal/mol at CASSCF(4,4)/cc-pVTZ level. The resulting 3CH2OO is less stable than the 1CH2OO. In this study, the biradical character (β) is used as a measure to understand the difference in the topology of the singlet and triplet PECs and the relation of the biradical nature of the species with their structures. The 3CH2OO has a larger biradical character than 1CH2OO, and because of the larger bond order of 1CH2OO, the C-O covalent bond becomes harder to break, thereby stabilizing 1CH2OO. Thus, this study provides insights into the shape of the PEC obtained from the reaction between 3CH2 and 3O2 in terms of their bonding nature and from the shape of the curves, the temperature dependence or independence of the rate of the reaction is discussed.

Spin-symmetry adaptation to the Monte Carlo correction configuration interaction wave functions.

We propose a method to adapt the spin-symmetry to the Monte Carlo correction configuration interaction (MC3I) wave function which is expanded by the selected Slater determinants (SDs). The spin-symmetry of the MC3I wave function is usually broken because the Monte Carlo method is used to select the SDs, and this problem becomes worse as the electron correlation becomes stronger. In the present method, the S^2 operator is applied to the set of the SDs in the MC3I wave function iteratively until the set becomes closed under S^2. The spin-symmetry adapted MC3I wave functions are calculated by diagonalization of the Hamiltonian matrix which is spanned by the converged set of SDs. The present method is tested by the application to the excited states of C2 in the bond dissociation region and the 100 lowest states of [Fe2S2(SCH3)4]3-. The deviations of S (total spin angular momentum) of some states were too large to assign the electronic states in the original MC3I calculations, while all states have the correct S after spin-symmetry adaptation and become comparable with the full configuration interaction and density matrix renormalization group results. With the present spin-symmetry adaptation, the MC3I method becomes applicable to strong electron correlation systems.

Vibrationally-resolved excitation and dissociation collision strengths of AlO+ by electron-impact using the R-matrix method

The electron-impact calculations are reported for excitation and dissociation of AlO+ ion using the R-matrix method. Calculations are performed in the static-exchange (SE) and close-coupling (CC) approximation. Each target state in CC approximation is represented by a configuration interaction (CI) wavefunction that takes into account the correlation and polarisation effects. In CC approximation 14-target states are included in the trial wavefunction of the entire scattering system. Potential energy curves (PECs) for the first four low-lying states are generated using the basis functions 6-311G* wherein we obtain X1Σ+ as the ground state contrary to a3Π as stated elsewhere in literature. Scattering calculations are then performed to yield vibrationally-resolved electronic excitation collision strengths to the first three lowest excited states a3Π, A1Π and b3Σ+. Using more accurate PECs we calculated the Franck–Condon factors which were then employed to get the vibrationally-resolved electronic excitations and dissociation collision strengths for the fragment channel Al++O of the lowest three excited states a3Π, A1Π and b3Σ+. All scattering calculations are performed at the experimental bond length 1.6178 A of AlO+. Rotational excitation cross sections (0→j, j = 1, 2 … 5) have also been calculated and the corresponding rate coefficients have been evaluated for excitation and de-excitation by using the Maxwellian distribution function for electron temperature upto 5000 K. There are many Feshbach resonances detected in this work. We have analysed only the low-lying resonances below the excitation threshold of A1Π excited state. Beyond this threshold the resonance structure is too complex to analyse due to many overlapping resonances.

Vibronic and spin-orbit coupling effects in the absorption spectra of pyrazine: A quantum chemical approach

Derivatives of dipole transition moments between spin?orbit coupled (SOC) multireference configuration interaction wave functions have been used in conjunction with vibrational frequencies from density functional theories to compute vibronic S1?S0 (11B3u11Ag ) and T1?S0 (13B3u?11Ag) absorption spectra in Herzberg?Teller approximation. The experimentally known spectra are well reproduced. The calculations reveal unexpectedly small spin?orbit couplings between the 13B3u (3n?*) state and nearby optically bright 1B2u (1??*) states, thus explaining the absence of the 1b1g10 (v10a10 ) fundamental in the vibrational fine-structure of the T1?S0 transition. Adiabatically, two triplet states are found below the S1 state. The out-of-plane distorted T2 minimum results from a pseudo Jahn?Teller interaction between two 3??* states of B1u and B2u symmetry. At the D2h-symmetric S0 and S1 minimum geometries, the latter states are located well above S1. The S1 and T2 potentials intersect at geometries far away from the Franck?Condon region. This explains the apparently contradictory results that the linewidth in the higher energy regime above the T1?S0 origin suddenly broadens while no trace of a second triplet state, located energetically below the S1 origin, could be identified in phosphorescence excitation spectra of the ultracold isolated pyrazine molecule.

Open-shell coupled-cluster valence-bond theory augmented with an independent amplitude approximation for three-pair correlations: Application to a model oxygen-evolving complex and single molecular magnet.

We report the failure of coupled-cluster valence-bond (CCVB) theory with two-pair configurations [D. W. Small and M. Head-Gordon, J. Chem. Phys. 130, 084103 (2009)] for open-shell (OS) spin-frustrated systems where including three-pair configurations is necessary to properly describe strong spin-correlations. We extend OS-CCVB by augmenting the model with three-pair configurations within the independent amplitude approximation. The resulting new electronic structure model, OS-CCVB+i3, involves only a quadratic number of independent wavefunction parameters. It includes the recently reported closed-shell CCVB+i3 as a special case. Its cost is dominated by integral transformations, and it is capable of breaking multiple bonds exactly for all systems examined so far. The strength of OS-CCVB+i3 is highlighted in realistic systems including the [CaMn3O4] cubane subunit of the oxygen-evolving complex and a molecular magnet with the [Cr9] core unit as well as model systems such as N3, V3O3, and P5. We show that OS-CCVB+i3 is only slightly dependent on the underlying perfect-pairing reference, while OS-CCVB shows a stronger dependence. We also emphasize the compactness of the OS-CCVB+i3 wavefunction compared to the heat-bath configuration interaction wavefunction, a recently introduced soft exponential-scaling approach.

Diffusion and reptation quantum Monte Carlo study of the NaK molecule

ABSTRACTDiffusion Monte Carlo (DMC) and Reptation Monte Carlo (RMC) methods, have been applied to study some properties of the NaK molecule. Hartree–Fock (HF), Density Functional (DFT) and single and double configuration interaction (SDCI) wavefunctions with a valence quadruple zeta atomic natural orbital (VQZ/ANO) basis set were used as trial wavefunctions. Values for the potential energy curve, dissociation energy and dipole moment were calculated for all methods and compared with experimental results and previous theoretical derivations. Quantum Monte Carlo (QMC) calculations were shown to be useful methods to recover correlation in NaK, essential to obtain a reasonable description of the molecule. The equilibrium distance yield a value close to the experimental one. The dissociation energy, however, is not so good, and the minimum error is about 4% of the experimental value, except when a coupled-clusters method is used. In this case, a conventional CCSD(T) calculation with an extended aug-pc-4 basis set gives a much better agreement to experiment. However, neither the CCSD(T) nor other MO and DFT methods are able to reproduce correctly the large dipole moment of this molecule. Even DMC methods with a simple HF trial wavefunction are able to give a better agreement to experiment, although they have a larger error bar.