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A parallel, distributed memory implementation of the adaptive sampling configuration interaction method

The many-body simulation of quantum systems is an active field of research that involves several different methods targeting various computing platforms. Many methods commonly employed, particularly coupled cluster methods, have been adapted to leverage the latest advances in modern high-performance computing. Selected configuration interaction (sCI) methods have seen extensive usage and development in recent years. However, the development of sCI methods targeting massively parallel resources has been explored only in a few research works. Here, we present a parallel, distributed memory implementation of the adaptive sampling configuration interaction approach (ASCI) for sCI. In particular, we will address the key concerns pertaining to the parallelization of the determinant search and selection, Hamiltonian formation, and the variational eigenvalue calculation for the ASCI method. Load balancing in the search step is achieved through the application of memory-efficient determinant constraints originally developed for the ASCI-PT2 method. The presented benchmarks demonstrate near optimal speedup for ASCI calculations of Cr 2 (24e, 30o) with 10 6 , 10 7 , and 3 × 10 8 variational determinants on up to 16 384 CPUs. Importantly, to the best of the authors’ knowledge, this is the largest variational ASCI calculation to date.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electric dipole moment of diatomic molecules by configuration interaction. V - Two states of /2/Sigma/+/ symmetry in CN.

Previous accurate dipole moment calculation techniques are modified to be applicable to higher excited states of symmetry. The self-consistent fields and configuration interactions are calculated for the X(2)Sigma(+) and B(2)Sigma(+) states of CN. Spin hyperfine constants and spin density at the nucleus are considered in the context of one-electron operator properties. The values of the self-consistent field and configuration interaction for the spin density are compared with experimental values for several diatomic molecules.

Green, S.↗

Electric dipole moment of diatomic molecules by configuration interaction. IV.

The theory of basis set dependence in configuration interaction calculations is discussed, taking into account a perturbation model which is valid for small changes in the self-consistent field orbitals. It is found that basis set corrections are essentially additive through first order. It is shown that an error found in a previously published dipole moment calculation by Green (1972) for the metastable first excited state of CO was indeed due to an inadequate basis set as claimed.

Green, S.↗

Nonorthogonal Configuration Interaction for Singlet Fission: Beyond the Dimer

Non-orthogonal configuration interaction with fragment calculations are presented for a number of compounds that show singlet fission properties: (i) four perylene-diimide derivatives, (ii) crystalline pentacene and its (B,N)-substituted variant, and (iii) a regular and a distorted stack of three indolonaphthyridine molecules. The electronic couplings between the singlet excitonic states (S 1 ) and the singlet-coupled double triplet (T 1 T 1 ), the so-called singlet fission coupling, were computed from ensembles with two and three molecules, and except for some small deviations when charge transfer states were included, results are virtually the same. Ensembles of three molecules were used to study the mechanisms of triplet separation, double triplet diffusion, and singlet and triplet exciton diffusion. The calculations show that apart from the standard mechanism for the generation of two uncoupled triplet states (S 1 → T 1 T 1 → T 1 ...T 1 ), there are two other possible pathways: the direct generation from the singlet excitonic state (S 1 → T 1 ...T 1 ) and the process in which the excitonic state evolves in a superposition of T 1 T 1 and T 1 ...T 1 states. Furthermore, the electronic coupling for triplet diffusion is in general much smaller than for singlet diffusion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Numerically exact configuration interaction at quadrillion-determinant scale

The combinatorial growth of configuration interaction (CI) has long limited this formally exact quantum chemistry method to only the smallest molecules. Here, we report a numerically exact CI calculation exceeding one quadrillion (10 15 ) determinants, made possible by a lossless categorical compression strategy within the small-tensor-product distributed active space (STP-DAS) framework. This approach overcomes the traditional memory bottlenecks of CI by a numerically exact compression of the wavefunction representation and reformulating the most computationally demanding matrix–vector operations. Using this method, we performed a fully relativistic CI calculation of the ground state of HBrTe with over 10 15 complex-valued determinants in just 34.5 h on 1000 computing nodes—the largest CI calculation ever reported. We further achieved fast computation for systems with hundreds of billions of determinants on only a few compute nodes. Extensive benchmarks confirm that the method retains full numerical exactness while cutting memory and computational cost by orders of magnitude. Compared to previous state-of-the-art CI calculations, this work achieves a 1000 times increase in CI space, a 10 6 -fold increase in floating-point operations performed, and a 10 6 -fold improvement in computational speed.

Computational chemistry↗

Ionization of HCCI Neutral and Cations by Strong Laser Fields Simulated With Time Dependent Configuration Interaction

Strong field ionization of neutral iodoacetylene (HCCI) can produce a coherent superposition of the X and A cations. This superposition results in charge migration between the CC π orbital and the iodine π-type lone pair which can be monitored by strong field ionization with short, intense probe pulses. Strong field ionization of the X and A states of HCCI cation was simulated with time-dependent configuration interaction using singly ionized configurations and singly excited, singly ionized configurations (TD-CISD-IP) and an absorbing boundary. Studies with static fields were used to obtain the 3-dimensional angular dependence of instantaneous ionization rates by strong fields and the orbitals involved in producing the cations and dications. The frequency of charge oscillation is determined by the energy separation of the X and A states; this separation can change depending on the direction and strength of the field. Furthermore, fields along the molecular axis can cause extensive mixing between the field-free X and A configurations. For coherent superpositions of the X and A states, the charge oscillations are characterized by two frequencies–the driving frequency of the laser field of the probe pulse and the intrinsic frequency due to the energy separation between the X and A states. For linear and circularly polarized pulses, the ionization rates show marked differences that depend on the polarization direction of the pulse, the carrier envelope phase and initial phase of the superposition. Varying the initial phase of the superposition at the beginning of the probe pulse is analogous to changing the delay between the pump and probe pulses. The charge oscillation in the coherent superposition of the X and A states results in maxima and minima in the ionization yield as a function of the superposition phase

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Two-Component Multireference Restricted Active Space Configuration Interaction for the Computation of L-Edge X-ray Absorption Spectra

X-ray absorption spectroscopy is a powerful probe of local electronic and nuclear structure, providing insights into chemical processes. The theoretical prediction and interpretation of metal L-edge X-ray absorption spectra is complicated by both relativistic effects, including spin-orbit coupling, and by the multiconfigurational nature of the states involved. This work details an exact two-component multireference restricted active space configuration interaction (X2C-MRRASCI) scheme that uses an exact two-component state average complete active space self-consistent-field method (X2C-SA-CASSCF), which includes the spin-orbit coupling in a variational manner, for the accurate description of the electronic structure before using a restricted active space configuration interaction method to describe the core excited states of the X-ray spectrum. Benchmark calculations are presented for a series of iron containing complexes, with results showing key features of the spectrum being reproduced, including ligand to metal charge transfer and shake-up excitations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Non-Orthogonal Configuration Interaction for Fragments

An overview is given of the non-orthogonal configuration interaction (NOCI) implementation in the open-source program GronOR. After pointing out the specifics of NOCI and its extension to ensembles of molecules NOCI-Fragments (NOCI-F), the theoretical foundations of the approaches are described. The introduction of a common molecular orbital basis, the selection of the most contributing determinants pairs, and a massively parallel and GPU-accelerated implementation have made possible the application of NOCI to medium-sized systems as illustrated in a short overview of some of the recent applications.

de Graaf, C.↗

GronOR: Scalable and Accelerated Nonorthogonal Configuration Interaction for Molecular Fragment Wave Functions

GronOR is a program package for nonorthogonal configuration interaction calculations. Electronic wave functions are constructed in terms of antisymmetrized products of multiconfiguration molecular fragment wave functions. The computational complexity of the nonorthogonal methodologies implemented in GronOR applied to large molecular assemblies requires a design that takes full advantage of massively parallel supercomputer architectures and accelerator technologies. This work describes the implementation strategy and resulting performance characteristics. In addition to parallelization and acceleration, the software development strategy includes aspects of fault resiliency and heterogeneous computing. The program was designed for large-scale supercomputers but also runs effectively on small clusters and workstations for small molecular systems. GronOR is available as open source to the scientific community.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Full configuration-interaction study of the ionic-neutral curve crossing in LiF

Full configuration-interaction (FCI) calculations are used to assess the relative ability of methods for truncating the n-particle expansion in describing the ionic-neutral curve crossing between the two lowest Sigma(+) states of LiF. While the FCI calculations yield a smooth dipole moment function, MRCI calculations based on CASSCF orbitals optimized for the lowest state at all r values yield a discontinuous dipole moment function. However, when the orbitals are optimized using a state-averaged CASSCF procedure, with equal weights for the ionic and neutral solutions, both the CASSCF and MRCI dipole moment functions are smooth and in reasonable agreement with the FCI. No single-reference-based method is found to work satisfactorily. Potential curves for the lowest two Sigma(+) states are determined in both the adiabatic and diabatic representations using a large atomic natural orbit Gaussian basis set and a state-averaged CASSCF/MRCI treatment of electron correlation.

Bauschlicher, Charles W., Jr.↗

A Doubles Correction to Electronic Excited States from Configuration Interaction in the Space of Single Substitutions

A perturbative correction to the method of configuration interaction with single substitutions (CIS) is presented. This CIS(D) correction approximately introduces the effect of double substitutions which are absent in CIS excited states. CIS(D) is a second-order perturbation expansion of the coupled-cluster excited state method, restricted to single and double substitutions, in a series in which CIS is zeroth order, and the first-order correction vanishes. CIS (D) excitation energies are size consistent and the calculational complexity scales with the fifth power of molecular size, akin to second-order Moller-Plesset theory for the ground state. Calculations on singlet excited states of ethylene, formaldehyde, acetaldehyde, butadiene and benzene show that CIS (D) is a uniform improvement over CIS. CIS(D) appears to be a promising method for examining excited states of large molecules, where more accurate methods are not feasible.

Head-Gordon, Martin↗

Relativistic Configuration-Interaction and Perturbation Theory Calculations for Heavy Atoms

Heavy atoms present challenges to atomic theory calculations due to the large number of electrons and their complicated interactions. Conventional approaches such as calculations based on Cowan’s code are limited and require a large number of parameters for energy agreement. One promising approach is relativistic configuration-interaction and many-body perturbation theory (CI-MBPT) methods. We present CI-MBPT results for various atomic systems where this approach can lead to reasonable agreement: La I, La II, Th I, Th II, U I, Pu II. Among atomic properties, energies, g-factors, electric dipole moments, lifetimes, hyperfine structure constants, and isotopic shifts are discussed. While in La I and La II accuracy for transitions is better than that obtained with other methods, more work is needed for actinides.

74 ATOMIC AND MOLECULAR PHYSICS↗

Tutorial for Non-Orthogonal Configuration Interaction Fragment Studies Using GronOR

A brief tutorial is presented for the GronOR non-orthogonal configuration interaction application illustrating the download and build process, setting up calculations with OpenMolcas and GronOR, and a description of the file structure and input options. An overview of the computational workflow includes the generation of fragment wave functions and integrals with an adapted version of OpenMolcas, running GronOR calculations, and accounting for dynamic correlation corrections. Three end-to-end use cases are provided, representing a molecular dimer, an ion pair, and overlapping molecular fragments.

Straatsma, T.P.↗

High-level coupled-cluster energetics by merging moment expansions with selected configuration interaction

Inspired by our earlier semi-stochastic work aimed at converging high-level coupled-cluster (CC) energetics, we propose a novel form of the CC(P; Q) theory in which the stochastic Quantum Monte Carlo propagations, used to identify dominant higher-than-doubly excited determinants, are replaced by the selected configuration interaction (CI) approach using the perturbative selection made iteratively (CIPSI) algorithm. The advantages of the resulting CIPSI-driven CC(P; Q) methodology are illustrated by a few molecular examples, including the dissociation of F 2 and the automerization of cyclobutadiene, where we recover the electronic energies corresponding to the CC calculations with a full treatment of singles, doubles, and triples based on the information extracted from compact CI wave functions originating from relatively inexpensive Hamiltonian diagonalizations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Relativistic K-LL Auger spectra in the intermediate-coupling scheme with configuration interaction

Theoretical K-LL Auger spectra from relativistic Dirac-Hartree-Slater calculations in intermediate coupling with configuration interaction (ICWCI) are considered. Calculated transition rates for 25 elements with Z between 18 and 96, inclusive, are listed and compare well with experimental data. Relativistic effects are found to be important above Z equal to about 35, and ICWCI is necessary to describe the spectra for Z less than about 60.

Chen, M. H.↗

Comparison of the quadratic configuration interaction and coupled cluster approaches to electron correlation including the effect of triple excitations

The recently proposed quadratic configuration interaction (QCI) method is compared with the more rigorous coupled cluster (CC) approach for a variety of chemical systems. Some of these systems are well represented by a single-determinant reference function and others are not. The finite order singles and doubles correlation energy, the perturbational triples correlation energy, and a recently devised diagnostic for estimating the importance of multireference effects are considered. The spectroscopic constants of CuH, the equilibrium structure of cis-(NO)2 and the binding energies of Be3, Be4, Mg3, and Mg4 were calculated using both approaches. The diagnostic for estimating multireference character clearly demonstrates that the QCI method becomes less satisfactory than the CC approach as non-dynamical correlation becomes more important, in agreement with a perturbational analysis of the two methods and the numerical estimates of the triple excitation energies they yield. The results for CuH show that the differences between the two methods become more apparent as the chemical systems under investigation becomes more multireference in nature and the QCI results consequently become less reliable. Nonetheless, when the system of interest is dominated by a single reference determinant both QCI and CC give very similar results.

Taylor, Peter R.↗