Full Configuration Interaction Research Articles

Accurate ab initio calculations of adiabatic energy and dipole moment: Prospects for the formation of cold Alkaline-Earth-Francium molecular ions ALKE-Fr+ (ALKE = Be, Mg, Ca, and Sr)

Alkaline-earth and alkali-metal mixtures have an electronic structure that is perfect for laser cooling. This makes them highly attractive for trapping and laser cooling experiments, allowing the formation of cold molecules. For this object, potential-energy curves and relevant spectroscopic parameters of the low-lying electronic excited states of 1,3Σ+, 1,3Π, and 1,3Δ symmetries of molecular-ion systems composed of alkaline-earth-ion and Francium alkali-metal-atom: ALKE-Fr+ (ALKE = Be, Mg, Ca and Sr), are determined using advanced theoretical technique in quantum chemistry, including a non-empirical pseudopotential, core-valence correlation, large Gaussian basis sets and Full Configuration Interaction (FCI). In order to obtain a more accurate understanding of the electronic structure of these systems, we also determined transition and permanent dipole moments and vibrational properties. Thereafter, the spontaneous and the black-body stimulated transition rates were determined and were employed to calculate lifetimes for all vibrational states of the ground electronic states 11Σ+ of molecular-ions under consideration. For the first and the second excited states, radiative lifetimes were investigated via the Franck–Condon approximation including bound-bound and bound-free transitions. High diagonal structure and large Franck Condon Factor (FCF) values f 00 = 0.987, f 11 = 0.959 and f 22 = 0.919 were obtained for the 11Π (v′ = 0, 1, 2)→ 11Σ+ (v = 0, 1, 2) transition making the BeFr+ system a good candidate for laser cooling. Furthermore, the current results could be used to investigate elastic scattering properties in cold-ion-atom collisions for the first excited states and may help the experimentalists for possible formation, spectroscopy, and photoassociation of cold ion-atom mixtures.

Coordinate Descent Full Configuration Interaction for Excited States.

An efficient excited state method, named xCDFCI, in the configuration interaction framework is proposed. xCDFCI extends the unconstrained nonconvex optimization problem in coordinate descent full configuration interaction (CDFCI) to a multicolumn version for low-lying excited states computation. The optimization problem is addressed via a tailored coordinate descent method. In each iteration, a determinant is selected based on an approximated gradient, and coefficients of all states associated with the selected determinant are updated. A deterministic compression is applied to limit memory usage. We test xCDFCI applied to H2O and N2 molecules under the cc-pVDZ basis set. For both systems, five low-lying excited states in the same symmetry sector are calculated, together with the ground state. xCDFCI also produces accurate binding curves of the carbon dimer in the cc-pVDZ basis with chemical accuracy, where the ground state and four excited states in the same symmetry sector are benchmarked.

What can lattice DFT teach us about real-space DFT?

In this paper we establish a connection between density functional theory (DFT) for lattice models and common real-space DFT. We consider the lattice DFT description of a two-level model subject to generic interactions in Mermin's DFT formulation in the grand canonical ensemble at finite temperature. The case of only density-density and Hund's rule interaction studied in earlier work is shown to be equivalent to an exact-exchange description of DFT in the real-space picture. In addition, we also include the so-called pair-hopping interaction which can be treated analytically and, crucially, leads to non-integer occupations of the Kohn-Sham (KS) levels even in the limit of zero temperature. Treating the hydrogen molecule in a minimal basis is shown to be equivalent to our two-level lattice DFT model. By means of the fractional occupations of the KS orbitals (which, in this case, are identical to the many-body ones) we reproduce the results of full configuration interaction, even in the dissociation limit and without breaking the spin symmetry. Beyond the minimal basis, we embed our HOMO-LUMO model into a standard DFT calculation and, again, obtain results in overall good agreement with exact ones without the need of breaking the spin symmetry.

Machine learning electronic structure methods based on the one-electron reduced density matrix

The theorems of density functional theory (DFT) establish bijective maps between the local external potential of a many-body system and its electron density, wavefunction and, therefore, one-particle reduced density matrix. Building on this foundation, we show that machine learning models based on the one-electron reduced density matrix can be used to generate surrogate electronic structure methods. We generate surrogates of local and hybrid DFT, Hartree-Fock and full configuration interaction theories for systems ranging from small molecules such as water to more complex compounds like benzene and propanol. The surrogate models use the one-electron reduced density matrix as the central quantity to be learned. From the predicted density matrices, we show that either standard quantum chemistry or a second machine-learning model can be used to compute molecular observables, energies, and atomic forces. The surrogate models can generate essentially anything that a standard electronic structure method can, ranging from band gaps and Kohn-Sham orbitals to energy-conserving ab-initio molecular dynamics simulations and infrared spectra, which account for anharmonicity and thermal effects, without the need to employ computationally expensive algorithms such as self-consistent field theory. The algorithms are packaged in an efficient and easy to use Python code, QMLearn, accessible on popular platforms.

Approximate Excited-State Geometry Optimization with the State-Averaged Adaptive Sampling Configuration Interaction Algorithm with Large Active Spaces.

The selected configuration interaction (SCI) wave function is a useful approximation to the full configuration interaction (FCI) one. The adaptive sampling CI (ASCI) method is a deterministic SCI method. By combining ASCI and orbital optimization, the ASCI self-consistent field (ASCI-SCF) method, which is an approximation of the complete active space self-consistent field (CASSCF) method, can be formulated as well. However, their applicability has been tested mainly on the systems in their electronically ground states. In this work, we implement the state-average (SA) ansatz in ASCI-SCF calculations to calculate excited states. We also derive expressions for the approximate analytical gradient and implement them as a computer program. We demonstrate the applicability of the current method for calculating vertical and adiabatic excitation energies and optimizing the molecular geometries of thermally activated delayed fluorescence (TADF) molecules.

Leveling the Mountain Range of Excited-State Benchmarking through Multistate Density Functional Theory.

The performance of multistate density functional theory (MSDFT) with nonorthogonal state interaction (NOSI) is assessed for 100 vertical excitation energies against the theoretical best estimates extracted to the full configuration interaction accuracy on the database developed by Loos et al. in 2018 (Loos2018). Two optimization techniques, namely, block-localized excitation and target state optimization, are examined along with two ways of estimating the transition density functional (TDF) for the correlation energy of the Hamiltonian matrix density functional. The results from the two optimization methods are similar. It was found that MSDFT-NOSI using the spin-multiplet degeneracy constraint for the TDF of spin-coupling interaction, along with the M06-2X functional, yields a root-mean-square error (RMSE) of 0.22 eV, which performs noticeably better than time-dependent density functional theory (DFT) at an RMSE of 0.43 eV using the same functional and basis set on the Loos2018 database. In comparison with wave function theory, NOSI has smaller errors than CIS(D∞), LR-CC2, and ADC(3) all of which have an RMSE of 0.28 eV, but somewhat greater than STEOM-CCSD (RMSE of 0.14 eV) and LR-CCSD (RMSE of 0.11 eV) wave function methods. In comparison with Kohn-Sham (KS) DFT calculations, the multistate DFT approach has little double counting of correlation. Importantly, there is no noticeable difference in the performance of MSDFT-NOSI on the valence, Rydberg, singlet, triplet, and double-excitation states. Although the use of another hybrid functional PBE0 leads to a greater RMSE of 0.36 eV, the deviation is systematic with a linear regression slope of 0.994 against the results with M06-2X. The present benchmark reveals that density functional approximations developed for KS-DFT for the ground state with a noninteracting reference may be adopted in MSDFT calculations in which the state interaction is key.

Generalization of the Tensor Product Selected CI Method for Molecular Excited States.

In a recent paper [JCTC, 2020, 16, 6098], we introduced a new approach for accurately approximating full CI ground states in large electronic active-spaces called Tensor Product Selected CI (TPSCI). In TPSCI, a large orbital active space is first partitioned into disjoint sets (clusters) for which the exact, local many-body eigenstates are obtained. Tensor products of these locally correlated many-body states are taken as the basis for the full, global Hilbert space. By folding correlation into the basis states themselves, the low-energy eigenstates become increasingly sparse, creating a more compact selected CI expansion. While we demonstrated that this approach can improve accuracy for a variety of systems, there is even greater potential for applications to excited states, particularly those which have some excited-state character. In this paper, we report on the accuracy of TPSCI for excited states, including a far more efficient implementation in the Julia programming language. In traditional SCI methods that use a Slater determinant basis, accurate excitation energies are obtained only after a linear extrapolation and at a large computational cost. We find that TPSCI with perturbative corrections provides accurate excitation energies for several excited states of various polycyclic aromatic hydrocarbons with respect to the extrapolated result (i.e., near exact result). Further, we use TPSCI to report highly accurate estimates of the lowest 31 eigenstates for a tetracene tetramer system with an active space of 40 electrons in 40 orbitals, giving direct access to the initial bright states and the resulting 18 doubly excited (biexcitonic) states.

Accurate and efficient calculations of Hellmann-Feynman forces for quantum computation.

First-order derivatives of energies with respect to atomic coordinates are widely computed and used in quantum chemistry simulations. The rapidly emerging technology of quantum computing offers a new paradigm for solving relevant quantum chemistry equations. In this work, we have achieved analytical calculations of atomic forces based on the Hellmann-Feynman theorem within the framework of the variational quantum eigensolver. The accuracy of the approach is demonstrated by calculating the atomic forces of H2, LiH, H2O, and NH3 molecules, which are in excellent agreement with values obtained from full configuration interaction calculations. In particular, for systems with degenerate molecular orbitals, the analytical approach has a significant accuracy advantage over finite-difference-based methods and will not involve additional computational effort on a quantum computer. The calculated forces are further used to optimize the geometries of NH3 and CH4 molecules and to perform abinitio molecular dynamics simulations for the umbrella inversion of NH3, demonstrating the feasibility of the approach in practical quantum chemistry simulations.

Benchmarking boron cluster calculations: Establishing reliable geometrical and energetic references for Bn (n = 1-4).

Using full configuration interaction (FCI) and multi-reference configuration interaction methods (MRCI), reliable geometrical and energetic references for Bn (n = 1-4) clusters were established. The accuracy of the computed results was confirmed by comparison with available experimental data. Benchmark calculations indicated that B97D3, B97D, VSXC, HCTH407, BP86 and CCSD(T) methods provided reasonable results for structural parameters, with mean absolute error (MAEs) within 0.020 Å. Among the tested density functional theory (DFT) methods, the VSXC functional showed the best performance in predicting the relative energies of B1 B4 with a MAE of 12.8 kJ mol-1 . Besides, B1B95, B971, TPSS, B3LYP, and BLYP functionals exhibited reasonable performance with MAE values of less than 15.0 kJ mol-1 . T1 diagnostic values between 0.035 and 0.109 at the CCSD(T) level revealed strong correlations in B2 B4 clusters, highlighting the need for caution in using CCSD(T) as an energy reference for small boron clusters. The methods of CCSDT, CCSDT(Q) and CCSDT[Q], which incorporate three-electron and four-electron excitations, effectively improved the accuracy of the energy calculations.

Electronic Free Energy Surface of the Nitrogen Dimer Using First-Principles Finite Temperature Electronic Structure Methods.

We use full configuration interaction and density matrix quantum Monte Carlo methods to calculate the electronic free energy surface of the nitrogen dimer within the free-energy Born-Oppenheimer approximation. As the temperature is raised from T = 0, we find a temperature regime in which the internal energy causes bond strengthening. At these temperatures, adding in the entropy contributions is required to cause the bond to gradually weaken with increasing temperature. We predict a thermally driven dissociation for the nitrogen dimer between 22,000 to 63,200 K depending on symmetries and basis set. Inclusion of more spatial and spin symmetries reduces the temperature required. The origin of these observations is explored using the structure of the density matrix at various temperatures and bond lengths.

Exchange correlation potentials from full configuration interaction in a Slater orbital basis.

Ryabinkin-Kohut-Staroverov (RKS) theory builds a bridge between wave function theory and density functional theory by using quantities from the former to produce accurate exchange-correlation potentials needed by the latter. In this work, the RKS method is developed and tested alongside Slater atomic orbital basis functions for the first time. To evaluate this approach, full configuration interaction computations in the Slater orbital basis are employed to give quality input to RKS, allowing full correlation to be present along with correct nuclei cusps and asymptotic decay of the wavefunction. SlaterRKS is shown to be an efficient algorithm to arrive at exchange-correlation potentials without unphysical artifacts in moderately-sized basis sets. Furthermore, enforcement of the nuclear cusp conditions will be shown to be vital for the success of the Slater-basis RKS method. Examples of weakly and strongly correlated molecular systems will demonstrate the main features of SlaterRKS.

Unitary Coupled Cluster: Seizing the Quantum Moment.

Shallow, CNOT-efficient quantum circuits are crucial for performing accurate computational chemistry simulations on current noisy quantum hardware. Here, we explore the usefulness of noniterative energy corrections, based on the method of moments of coupled-cluster theory, for accelerating convergence toward full configuration interaction. Our preliminary numerical results relying on iteratively constructed ansätze suggest that chemically accurate energies can be obtained with substantially more compact circuits, implying enhanced resilience to gate and decoherence noise.

Classical and quantum trial wave functions in auxiliary-field quantum Monte Carlo applied to oxygen allotropes and a CuBr2 model system.

In this work, we test a recently developed method to enhance classical auxiliary-field quantum Monte Carlo (AFQMC) calculations with quantum computers against examples from chemistry and material science, representative of classes of industry-relevant systems. As molecular test cases, we calculate the energy curve of H4 and the relative energies of ozone and singlet molecular oxygen with respect to triplet molecular oxygen, which is industrially relevant in organic oxidation reactions. We find that trial wave functions beyond single Slater determinants improve the performance of AFQMC and allow it to generate energies close to chemical accuracy compared to full configuration interaction or experimental results. In the field of material science, we study the electronic structure properties of cuprates through the quasi-1D Fermi-Hubbard model derived from CuBr2, where we find that trial wave functions with both significantly larger fidelities and lower energies over a mean-field solution do not necessarily lead to AFQMC results closer to the exact ground state energy.

Assessment of DFT functionals for a minimal nitrogenase [Fe(SH)4H]- model employing state-of-the-art abinitio methods.

We have designed a [Fe(SH)4H]- model with the fifth proton binding either to Fe or S. We show that the energy difference between these two isomers (∆E) is hard to estimate with quantum-mechanical (QM) methods. For example, different density functional theory (DFT) methods give ∆E estimates that vary by almost 140 kJ/mol, mainly depending on the amount of exact Hartree-Fock included (0%-54%). The model is so small that it can be treated by many high-level QM methods, including coupled-cluster (CC) and multiconfigurational perturbation theory approaches. With extrapolated CC series (up to fully connected coupled-cluster calculations with singles, doubles, and triples) and semistochastic heat-bath configuration interaction methods, we obtain results that seem to be converged to full configuration interaction results within 5 kJ/mol. Our best result for ∆E is 101 kJ/mol. With this reference, we show that M06 and B3LYP-D3 give the best results among 35 DFT methods tested for this system. Brueckner doubles coupled cluster with perturbaitve triples seems to be the most accurate coupled-cluster approach with approximate triples. CCSD(T) with Kohn-Sham orbitals gives results within 4-11 kJ/mol of the extrapolated CC results, depending on the DFT method. Single-reference CC calculations seem to be reasonably accurate (giving an error of ∼5 kJ/mol compared to multireference methods), even if the D1 diagnostic is quite high (0.25) for one of the two isomers.

Optimizing Jastrow factors for the transcorrelated method.

We investigate the optimization of flexible tailored real-space Jastrow factors for use in the transcorrelated (TC) method in combination with highly accurate quantum chemistry methods, such as initiator full configuration interaction quantum Monte Carlo (FCIQMC). Jastrow factors obtained by minimizing the variance of the TC reference energy are found to yield better, more consistent results than those obtained by minimizing the variational energy. We compute all-electron atomization energies for the challenging first-row molecules C2, CN, N2, and O2 and find that the TC method yields chemically accurate results using only the cc-pVTZ basis set, roughly matching the accuracy of non-TC calculations with the much larger cc-pV5Z basis set. We also investigate an approximation in which pure three-body excitations are neglected from the TC-FCIQMC dynamics, saving storage and computational costs, and show that it affects relative energies negligibly. Our results demonstrate that the combination of tailored real-space Jastrow factors with the multi-configurational TC-FCIQMC method provides a route to obtaining chemical accuracy using modest basis sets, obviating the need for basis-set extrapolation and composite techniques.

A quantum computing implementation of nuclearelectronic orbital (NEO) theory: Toward an exact pre-Born-Oppenheimer formulation of molecular quantum systems.

Nuclear quantum phenomena beyond the Born-Oppenheimer approximation are known to play an important role in a growing number of chemical and biological processes. While there exists no unique consensus on a rigorous and efficient implementation of coupled electron-nuclear quantum dynamics, it is recognized that these problems scale exponentially with system size on classical processors and, therefore, may benefit from quantum computing implementations. Here, we introduce a methodology for the efficient quantum treatment of the electron-nuclear problem on near-term quantum computers, based upon the Nuclear-Electronic Orbital (NEO) approach. We generalize the electronic two-qubit tapering scheme to include nuclei by exploiting symmetries inherent in the NEO framework, thereby reducing the Hamiltonian dimension, number of qubits, gates, and measurements needed for calculations. We also develop parameter transfer and initialization techniques, which improve convergence behavior relative to conventional initialization. These techniques are applied to H2 and malonaldehyde for which results agree with NEO full configuration interaction and NEO complete active space configuration interaction benchmarks for ground state energy to within 10-6 hartree and entanglement entropy to within 10-4. These implementations therefore significantly reduce resource requirements for full quantum simulations of molecules on near-term quantum devices while maintaining high accuracy.

Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data.

We present a machine learning approach to calculating electronic specific heat capacities for a variety of benchmark molecular systems. Our models are based on data from density matrix quantum Monte Carlo, which is a stochastic method that can calculate the electronic energy at finite temperature. As these energies typically have noise, numerical derivatives of the energy can be challenging to find reliably. In order to circumvent this problem, we use Gaussian process regression to model the energy and use analytical derivatives to produce the specific heat capacity. From there, we also calculate the entropy by numerical integration. We compare our results to cubic splines and finite differences in a variety of molecules in which Hamiltonians can be diagonalized exactly with full configuration interaction. We finally apply this method to look at larger molecules where exact diagonalization is not possible and make comparisons with more approximate ways to calculate the specific heat capacity and entropy.

Transcorrelated coupled cluster methods. II. Molecular systems.

We demonstrate the accuracy of ground-state energies of the transcorrelated Hamiltonian, employing sophisticated Jastrow factors obtained from variational Monte Carlo, together with the coupled cluster and distinguishable cluster methods at the level of singles and doubles excitations. Our results show that already with the cc-pVTZ basis, the transcorrelated distinguishable cluster method gets close to the complete basis limit and near full configuration interaction quality values for relative energies of over thirty atoms and molecules. To gauge the performance in different correlation regimes, we also investigate the breaking of the nitrogen molecule with transcorrelated coupled cluster methods. Numerical evidence is presented to further justify an efficient way to incorporate the major effects coming from the three-body integrals without explicitly introducing them into the amplitude equations.

Another Torture Track for Quantum Chemistry: Reinvestigation of the Benzaldehyde Amidation by Nitrogen‐Atom Transfer from Platinum(II) and Palladium(II) Metallonitrenes

AbstractWe showcase here a dramatic failure of CCSD(T) theory that originates from the pronounced multi‐reference character of a key intermediate formed in the benzaldehyde amidation by N‐atom transfer from Pd(II) and Pt(II) metallonitrenes studied recently in combined experimental and theoretical work. For detailed analysis we devised a minimal model system, for which we established reliable reference energies based on approximate full configuration interaction theory, to assess the performance of single‐reference coupled‐cluster theory up to the CCSDTQ(P) excitation level. While RHF‐based CCSD(T) theory suffered dramatic errors, in one case exceeding 220 kcal mol−1, we show that the use of broken‐symmetry (BS) or Kohn‐Sham (KS) orbital references yields substantially improved CCSD(T) results. Further, the EOM‐SF‐CCSD(T)(a)* approach met the reference data with excellent accuracy. We applied the KS‐CCSD(T*)‐F12b variant as high‐level part of an ONIOM(KS‐CC:DFT) scheme to reinvestigate the reactivity of the full Pt(II) and Pd(II) metallonitrenes. The revised reaction pathway energetics provide a detailed mechanistic rationale for the experimental observations.

Magnetic Interactions in a [Co(II)3Er(III)(OR)4] Model Cubane through Forefront Multiconfigurational Methods

Strong electron correlation effects are one of the major challenges in modern quantum chemistry. Polynuclear transition metal clusters are peculiar examples of systems featuring such forms of electron correlation. Multireference strategies, often based on but not limited to the concept of complete active space, are adopted to accurately account for strong electron correlation and to resolve their complex electronic structures. However, transition metal clusters already containing four magnetic centers with multiple unpaired electrons make conventional active space based strategies prohibitively expensive, due to their unfavorable scaling with the size of the active space. In this work, forefront techniques, such as density matrix renormalization group (DMRG), full configuration interaction quantum Monte Carlo (FCIQMC), and multiconfiguration pair-density functional theory (MCPDFT), are employed to overcome the computational limitation of conventional multireference approaches and to accurately investigate the magnetic interactions taking place in a [Co(II)3Er(III)(OR)4] (chemical formula [Co(II)3Er(III)(hmp)4(μ2-OAc)2(OH)3(H2O)], hmp = 2-(hydroxymethyl)-pyridine) model cubane water oxidation catalyst. Complete active spaces with up to 56 electrons in 56 orbitals have been constructed for the seven energetically lowest different spin states. Relative energies, local spin, and spin-spin correlation values are reported and provide crucial insights on the spin interactions for this model system, pivotal in the rationalization of the catalytic activity of this system in the water-splitting reaction. A ferromagnetic ground state is found with a very small, ∼50 cm-1, highest-to-lowest spin gap. Moreover, for the energetically lowest states, S = 3-6, the three Co(II) sites exhibit parallel aligned spins, and for the lower states, S = 0-2, two Co(II) sites retain strong parallel spin alignment.