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Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo

Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, “replica” ensemble of walkers, whose population evolves in imaginary time independently from the first and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the Hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, the present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments, and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Configuration–Interaction Perturbation Theory Calculations of Pu II

Configuration–interaction perturbation theory (CI–PT) is applied to calculations of low-energy states of Pu II. This ion is quite challenging due to a large number of possible determinants arising from seven valence electrons and strong relativistic effects. The CI–PT calculations agree with experiments for the energies and g-factors for many low-energy states that allowed positive identification of the theoretical levels. Isotope shifts were also used to aid in identification, and, in case of the odd states, fitting with three independent parameters was used to match theoretical isotope shifts to the experimental values with good accuracy. The CI–PT approach tested here on the Pu II ion can be generally used to calculate properties of many complex atoms, including U I that can find application in fundamental and applied science.

74 ATOMIC AND MOLECULAR PHYSICS↗

Improved Fast Randomized Iteration Approach to Full Configuration Interaction

In this work, we present three modifications to our recently introduced fast randomized iteration method for full configuration interaction (FCI-FRI) and investigate their effects on the method’s performance for Ne, H 2 O, and N 2 . The initiator approximation, originally developed for full configuration interaction quantum Monte Carlo, significantly reduces statistical error in FCI-FRI when few samples are used in compression operations, enabling its application to larger chemical systems. The semistochastic extension, which involves exactly preserving a fixed subset of elements in each compression, improves statistical efficiency in some cases but reduces it in others. We also developed a new approach to sampling excitations that yields consistent improvements in statistical efficiency and reductions in computational cost. We discuss possible strategies based on our findings for improving the performance of stochastic quantum chemistry methods more generally.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Decomposition of the configuration-interaction coefficients in the multiconfiguration time-dependent Hartree-Fock method

An approximate implementation of the multiconfiguration time-dependent Hartree-Fock method is proposed, in which the matrix of configuration-interaction coefficients is decomposed into a product of matrices of smaller dimension. The applicability of this method in which all the configurations are kept in the expansion of the wave function, while the configuration-interaction coefficients are approximately calculated, is discussed by showing the results on three model systems: a one-dimensional model of a beryllium atom, a one-dimensional model of a carbon atom, and a one-dimensional model of a chain of four hydrogen atoms. The time-dependent electronic dynamics induced by a few-cycle, long-wavelength laser pulse is found to be well described at a lower computational cost compared to the standard multiconfiguration time-dependent Hartree-Fock treatment. Drawbacks of the method are also discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Non-orthogonal configuration interaction with single substitutions for the calculation of core-excited states

In this paper, we present the non-orthogonal configuration interaction singles (NOCIS) method for calculating core-excited states of closed-shell molecules. NOCIS is a black-box variant of NOCI, which uses A different core-ionized determinants for a molecule with A atoms of a given element to form single substitutions. NOCIS is a variational, spin-pure, size-consistent ab initio method that dramatically improves on standard CIS by capturing essential orbital relaxation effects, in addition to essential configuration interaction. We apply it to the calculation of core-excitations for several smaller molecules and demonstrate that it performs competitively with other Hartree-Fock and DFT-based methods. We also benchmark it in several basis sets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Benchmark Full Configuration-Interaction Calculations on HF and NH2

Full configuration-interaction (FCI) calculations are performed at selected geometries for the (sup 1)Sigma(+) state of HCF and the (sup 2)B(sub 1) and (sup 3)A(sub 1) states NH2 using both DZ and DZP Gaussian basis sets. Higher excitations become more important when the bonds are stretched and the SCF reference becomes a poorer zeroth-order description of the wave function. The CASSCF-MRCI procedure gives excellent agreement with the FCI potentials, especially when corrected with a multireference analog of the Davidson correction.

Bauschlicher, Charles W., Jr.↗

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↗

Influence of pseudopotentials on excitation energies from selected configuration interaction and diffusion Monte Carlo

Due to their diverse nature, the faithful description of excited states within electronic structure theory methods remains one of the grand challenges of modern theoretical chemistry. Quantum Monte Carlo (QMC) methods have been applied very successfully to ground state properties but still remain generally less effective than other non-stochastic methods for electronically excited states. Nonetheless, we have recently reported accurate excitation energies for small organic molecules at the fixed-node diffusion Monte Carlo (FN-DMC) within a Jastrow-free QMC protocol relying on a deterministic and systematic construction of nodal surfaces using the selected configuration interaction (sCI) algorithm known as CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively). Albeit highly accurate, these all-electron calculations are computationally expensive due to the presence of core electrons. One very popular approach to remove these chemically-inert electrons from the QMC simulation is to introduce pseudopotentials (also known as effective core potentials). Taking the water molecule as an example, we investigate the influence of Burkatzki-Filippi-Dolg (BFD) pseudopotentials and their associated basis sets on vertical excitation energies obtained with sCI and FN-DMC methods. Although these pseudopotentials are known to be relatively safe for ground state properties, we evidence that special care may be required if one strives for highly accurate vertical transition energies. Indeed, comparing all-electron and valence-only calculations, we show that using pseudopotentials with the associated basis sets can induce differences of the order of 0.05 eV on the excitation energies. Fortunately, a reasonable estimate of this shift can be estimated at the sCI level.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electronic spectra of azaindole and its excited state mixing: A symmetry-adapted cluster configuration interaction study

Electronic structures of azaindole were studied using symmetry-adapted cluster configuration interaction theory utilizing Dunning’s cc-pVTZ basis set augmented with appropriate Rydberg spd functions on carbon and nitrogen atoms. The results obtained in the present study show good agreement with the available experimental values. Importantly, and contrary to previous theoretical studies, the excitation energy calculated for the important n–π{sup ∗} state agrees well with the experimental value. A recent study by Pratt and co-workers concluded that significant mixing of π-π{sup ∗} and n-π{sup ∗} states leads to major change in the magnitude and direction of the dipole moment of the upper state vibrational level in the 0,0 + 280 cm{sup −1} band in the S{sub 1}←S{sub 0} transition when compared to that of the zero-point level of the S{sub 1} state. The present study, however, shows that all the four lowest lying excited states, {sup 1}L{sub b} π-π{sup ∗}, {sup 1}L{sub a} π-π{sup ∗}, n-π{sup ∗}, and π-σ{sup ∗}, cross each other in one way or another, and hence, significant state mixing between them is likely. The upper state vibrational level in the 0,0 + 280 cm{sup −1} band in the S{sub 1}←S{sub 0} transition benefits from this four-state mixing and this can explain the change in magnitude and direction of the dipole moment of the S{sub 1} excited vibrational level. This multistate mixing, and especially the involvement of π-σ{sup ∗} state in mixing, could also provide a route for hydrogen atom detachment reactions. The electronic spectra of benzimidazole, a closely related system, were also investigated in the present study.

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.↗

Controlling the high frequency response of H{sub 2} by ultra-short tailored laser pulses: A time-dependent configuration interaction study

We combine the stochastic pulse optimization (SPO) scheme with the time-dependent configuration interaction singles method in order to control the high frequency response of a simple molecular model system to a tailored femtosecond laser pulse. For this purpose, we use H{sub 2} treated in the fixed nuclei approximation. The SPO scheme, as similar genetic algorithms, is especially suited to control highly non-linear processes, which we consider here in the context of high harmonic generation. Here, we will demonstrate that SPO can be used to realize a “non-harmonic” response of H{sub 2} to a laser pulse. Specifically, we will show how adding low intensity side frequencies to the dominant carrier frequency of the laser pulse and stochastically optimizing their contribution can create a high-frequency spectral signal of significant intensity, not harmonic to the carrier frequency. At the same time, it is possible to suppress the harmonic signals in the same spectral region, although the carrier frequency is kept dominant during the optimization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Simulating Electron Dynamics of Complex Molecules with Time-Dependent Complete Active Space Configuration Interaction

In this paper, time-dependent electronic structure methods are growing in popularity as tools for modeling ultrafast and/or nonlinear processes, for computing spectra, and as the electronic structure component of mean-field molecular dynamics simulations. Time-dependent configuration interaction (TD-CI) offers several advantages over the widely used real-time time-dependent density functional theory: namely, that it correctly models Rabi oscillations; it offers a spin-pure description of open-shell systems; and a hierarchy of TD-CI methods can be defined that systematically approach the exact solution of the time-dependent Schrodinger equation (TDSE). In this work, we present a novel TD-CI approach that extends TD-CI to large complete active-space configuration expansions. Such extension is enabled by use of a direct configuration interaction approach that eliminates the need to explicitly build, store, or diagonalize the Hamiltonian matrix. Graphics processing unit (GPU) acceleration enables fast solution of the TDSE even for large active spaces—up to 12 electrons in 12 orbitals (853776 determinants) in this work. A symplectic split operator propagator yields long-time norm conservation. We demonstrate the applicability of our approach by computing the response of a large molecule with a strongly correlated ground state, decacene (C 42 H 24 ), to various pulses (δ-function, transform limited, chirped). Our simulations predict that chirped pulses can be used to induce dipole-forbidden transitions. Simulations of decacene using the 6-31G(d) basis set and a 12 electrons/12 orbitals active space took 20.1 h to propagate for 100 fs with a 1 attosecond time step on a single NVIDIA K40 GPU. Convergence with respect to time step is found to depend on the property being computed and the chosen active space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An excited-state approach within full configuration interaction quantum Monte Carlo

We present a new approach to calculate excited states with the full configuration interaction quantum Monte Carlo (FCIQMC) method. The approach uses a Gram-Schmidt procedure, instantaneously applied to the stochastically evolving distributions of walkers, to orthogonalize higher energy states against lower energy ones. It can thus be used to study several of the lowest-energy states of a system within the same symmetry. This additional step is particularly simple and computationally inexpensive, requiring only a small change to the underlying FCIQMC algorithm. No trial wave functions or partitioning of the space is needed. The approach should allow excited states to be studied for systems similar to those accessible to the ground-state method due to a comparable computational cost. As a first application, we consider the carbon dimer in basis sets up to quadruple-zeta quality and compare to existing results where available.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Relativistic configuration-interaction and many-body-perturbation-theory calculations of U i hyperfine constants

Neutral uranium (U i) is a very difficult atom for theoretical calculations due to a large number (six) of valence electrons, strong valence-valence and valence-core correlations, high density of states, and relativistic effects. Configuration-interaction many-body perturbation theory (CI-MBPT) can efficiently treat valence-core correlations and relativistic effects, but because the formalism was developed for a Dirac-Hartree-Fock (DHF) starting potential that does not contain valence electrons, quite large CI space is needed to compensate for the + 6 charge of such a potential. Much more efficient is the relativistic configuration-interaction (RCI) approach, which uses a relatively accurate starting DHF potential that includes some valence electrons to make the valence-electron Hamiltonian diagonally dominated for some states. Here we report calculations of U i hyperfine constants of several low-energy states using the RCI method with the starting potential that includes four f valence electrons. With this starting potential, it is possible to use the single-configuration approximation or small basis sets to obtain quite accurate results for hyperfine-structure constants. In fact, by scaling the nuclear magnetic moment, the agreement for five levels was within 5% and a new magnetic moment can be recommended, 0.43(2). When two states are mixed, it is difficult to predict the exact mixing fractions, so in this case we proposed a method in which the mixing fraction is found by optimization of one parameter in the MBPT correction to obtain correct g factors. The resulting hyperfine constants are significantly improved. Finally, the CI-MBPT approach was also tested, with some success for low-energy states, with the limited basis set. The methods investigated here can be further developed to include more extensive data sets to improve accuracy and can be applied to other atoms and for calculations of other properties, for example, relevant to fundamental symmetry tests.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

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↗