Coupled Hartree-Fock Perturbation Research Articles

Analytical Gradient Using Cluster-in-Molecule RI-MP2 Method for the Geometry Optimizations of Large Systems.

We present an efficient analytical energy gradient algorithm for the cluster-in-molecule resolution-of-identity second-order Møller-Plesset perturbation (CIM-RI-MP2) method based on the Lagrange multiplier method. Our algorithm independently constructs the Lagrangian formalism within each cluster, avoiding the solution of the coupled-perturbed Hartree-Fock (CPHF) equation for the whole system. Due to this feature, the computational cost of the CIM-RI-MP2 gradients is much lower than that of other local MP2 algorithms. Benchmark calculations of several molecules containing up to 312 atoms demonstrate the general applicability of our CIM-RI-MP2 gradient algorithm. The optimized structure of a 244-atom molecule using the CIM-RI-MP2 method with the cc-pVDZ basis set is in good agreement with the corresponding crystal structure. A single-point gradient calculation conducted for a molecular cage containing 972 atoms and 9612 basis functions takes 48 h on 25 nodes, utilizing a total of 600 CPU cores. The present CIM-RI-MP2 gradient program is applicable for obtaining the optimized geometries of large systems with hundreds of atoms.

The Effective Fragment Molecular Orbital Method: Achieving High Scalability and Accuracy for Large Systems.

The effective fragment molecular orbital (EFMO) method has been developed to predict the total energy of a very large molecular system accurately (with respect to the underlying quantum mechanical method) and efficiently by taking advantage of the locality of strong chemical interactions and employing a two-level hierarchical parallelism. The accuracy of the EFMO method is partly attributed to the accurate and robust intermolecular interaction prediction between distant fragments, in particular, the many-body polarization and dispersion effects, which require the generation of static and dynamic polarizability tensors by solving the coupled perturbed Hartree-Fock (CPHF) and time-dependent HF (TDHF) equations, respectively. Solving the CPHF and TDHF equations is the main EFMO computational bottleneck due to the inefficient (serial) and I/O-intensive implementation of the CPHF and TDHF solvers. In this work, the efficiency and scalability of the EFMO method are significantly improved with a new CPU memory-based implementation for solving the CPHF and TDHF equations that are parallelized by either message passing interface (MPI) or hybrid MPI/OpenMP. The accuracy of the EFMO method is demonstrated for both covalently bonded systems and noncovalently bound molecular clusters by systematically examining the effects of basis sets and a key distance-related cutoff parameter, Rcut. Rcut determines whether a fragment pair (dimer) is treated by the chosen ab initio method or calculated using the effective fragment potential (EFP) method (separated dimers). Decreasing the value of Rcut increases the number of separated (EFP) dimers, thereby decreasing the computational effort. It is demonstrated that excellent accuracy (<1 kcal/mol error per fragment) can be achieved when using a sufficiently large basis set with diffuse functions coupled with a small Rcut value. With the new parallel implementation, the total EFMO wall time is substantially reduced, especially with a high number of MPI ranks. Given a sufficient workload, nearly ideal strong scaling is achieved for the CPHF and TDHF parts of the calculation. For the first time, EFMO calculations with the inclusion of long-range polarization and dispersion interactions on a hydrated mesoporous silica nanoparticle with explicit water solvent molecules (more than 15k atoms) are achieved on a massively parallel supercomputer using nearly 1000 physical nodes. In addition, EFMO calculations on the carbinolamine formation step of an amine-catalyzed aldol reaction at the nanoscale with explicit solvent effects are presented.

Fragment-Based Deep Learning for Simultaneous Prediction of Polarizabilities and NMR Shieldings of Macromolecules and Their Aggregates.

Simultaneous prediction of the molecular response properties, such as polarizability and the NMR shielding constant, at a low computational cost is an unresolved issue. We propose to combine a linear-scaling generalized energy-based fragmentation (GEBF) method and deep learning (DL) with both molecular and atomic information-theoretic approach (ITA) quantities as effective descriptors. In GEBF, the total molecular polarizability can be assembled as a linear combination of the corresponding quantities calculated from a set of small embedded subsystems in GEBF. In the new GEBF-DL(ITA) protocol, one can predict subsystem polarizabilities based on the corresponding molecular wave function (thus electron density and ITA quantities) and DL model rather than calculate them from the computationally intensive coupled-perturbed Hartree-Fock or Kohn-Sham equations and finally obtain the total molecular polarizability via a linear combination equation. As a proof-of-concept application, we predict the molecular polarizabilities of large proteins and protein aggregates. GEBF-DL(ITA) is shown to be as accurate enough as GEBF, with mean absolute percentage error <1%. For the largest protein aggregate (>4000 atoms), GEBF-DL(ITA) gains a speedup ratio of 3 compared with GEBF. It is anticipated that when more advanced electronic structure methods are used, this advantage will be more appealing. Moreover, one can also predict the NMR chemical shieldings of proteins with reasonably good accuracy. Overall, the cost-efficient GEBF-DL(ITA) protocol should be a robust theoretical tool for simultaneously predicting polarizabilities and NMR shieldings of large systems.

Analytic Non-adiabatic Couplings for Selected Configuration Interaction via Approximate Degenerate Coupled Perturbed Hartree-Fock.

We use degenerate perturbation theory and assume that for degenerate pairs of orbitals, the coupled perturbed Hartree-Fock coefficients are symmetric in the degenerate basis to show [Formula: see text] is the only modification needed in the original molecular orbital basis. This enables us to develop efficient and accurate analytic nonadiabatic couplings between electronic states for selected configuration interactions (CIs). Even when the states belong to different irreducible representations, degenerate orbital pairs cannot be excluded by symmetry. For various excited states of carbon monoxide and trigonal planar ammonia, we benchmark the method against the full CI and find it to be accurate. We create a semi-numerical approach and use it to show that the analytic approach is correct even when a high-symmetry structure is distorted to break symmetry so that near degeneracies in orbitals occur. For a range of geometries of trigonal planar ammonia, we find that the analytic non-adiabatic couplings for selected CI can achieve sufficient accuracy using a small fraction of the full CI space.

First-principles calculations to investigate structural, electronic, optical and elastic properties of α-Ca3N2

The optoelectronic industry, which has become a cornerstone, requires a semiconductor compound to function as a sustainable and green energy source. In this connection, the present study provides a systematic approach to examine the electronic and optical properties of α-Ca3N2 using the linear combination of atomic orbitals method. The xc-functional BECKE-PBE gives the best results for electronic properties by describing the band gap correctly. The dispersion curve shows that α-Ca3N2 is a semiconductor with an indirect band gap of 1.33 eV along the H-Γ direction. Effective masses of electrons and holes are calculated at the peak of the lowest conduction band and highest valence band, along the Γ- direction. Calculation for optical properties has been performed using coupled-perturbed Hartree-Fock scheme for static values and phonon spectrum calculations are performed for dynamic dielectric functions. Further, frequency dependent electron loss function and reflectivity are determined from the dielectric functions. The elastic constants are estimated and elastic moduli are determined. Bulk modulus of 80.6 GPa and Poisson’s ratio of 0.275 reveals that α-Ca3N2 is a hard and ductile material. The characteristic properties of α-Ca3N2 make it a suitable candidate for optoelectronic applications.

A Density Functional Theory and Information-Theoretic Approach Study of Interaction Energy and Polarizability for Base Pairs and Peptides.

Using density functional theory (DFT) and the information-theoretic approach (ITA) quantities to appreciate the energetics and properties of biopolymers is still an unaccomplished and ongoing task. To this end, we studied the building blocks of nucleic acid base pairs and small peptides. For base pairs, we have dissected the relative importance of energetic components by using two energy partition schemes in DFT. Our results convincingly show that the exchange-correlation effect predominantly governs the molecular stability of base pairs while the electrostatic potential plays a minor but indispensable role, and the steric effect is trivial. Furthermore, we have revealed that simple density-based ITA functions are in good relationships with molecular polarizabilities for a series of 30 hydrogen-bonded base pairs and all 20 natural α-amino acids, 400 dipeptides, and 8000 tripeptides. Based on these lines, one can easily predict the molecular polarizabilities of larger peptides, even proteins as long as the total molecular wavefunction is available, rather than solving the computationally demanding coupled-perturbed Hartree–Fock (CPHF) equation or its DFT counterpart coupled-perturbed Kohn–Sham (CPKS) equation.

Quantum Perturbation Theory Using Tensor Cores and a Deep Neural Network.

Time-independent quantum response calculations are performed using Tensor cores. This is achieved by mapping density matrix perturbation theory onto the computational structure of a deep neural network. The main computational cost of each deep layer is dominated by tensor contractions, i.e., dense matrix-matrix multiplications, in mixed-precision arithmetics, which achieves close to peak performance. Quantum response calculations are demonstrated and analyzed using self-consistent charge density-functional tight-binding theory as well as coupled-perturbed Hartree-Fock theory. For linear response calculations, a novel parameter-free convergence criterion is presented that is well-suited for numerically noisy low-precision floating point operations and we demonstrate a peak performance of almost 200 Tflops using the Tensor cores of two Nvidia A100 GPUs.

Design rules for the large two-photon absorption diketopyrrolopyrrole-based quadrupolar symmetrical chromophores

Two-photon absorption of a series of symmetrical diketopyrrolopyrrole (DPP) derivatives is studied by means of density functional theory applied to second-order response function. Several important issues in modeling are highlighted which must be addressed for a reliable reproduction of the experimental results. A comparison of the theoretical results with the experimental ones indicates that the computed two-photon absorption (TPA) cross sections show a good agreement for the three-state model in case of symmetrical quadrupolar DPP derivatives with donor ending groups. Although the results of TPA cross section observed for the systems with strong electron accepting ending groups seem to be overestimated for the three-state model. At the same time using an algorithm for the direct calculation of the third-order processes by the solving dynamic coupled-perturbed Hartree–Fock equation shows relatively good qualitative results for both donor and acceptor ending groups; however, it was found to be less accurate quantitatively for the already published experimental results. Thus, to obtain a valid overview, supposedly, both methods have to be considered. In general, in the present paper, a strategy toward molecular tailoring of large TPA cross-sectional materials is described, which can be extremely useful tool to predict materials’ properties prior to synthesis and measurements.

Structural stability and vibrational analysis of beryllium sulfide BeS from the bulk to the (n,0) nanotubes. An ab initio description

Beryllium sulfide (BeS) in different forms from molecule, bulk, monolayer (h-BeS), to the single-walled nanotube obtained by wrapping the h-BeS monolayer along the (n,0) hexagonal lattice vector for n varying from n = 6 to 64, has been examined. Density functional theory (DFT) with an all electron basis set and the hybrid DFT/B3LYP level have been applied to compute energetic and geometrical, electronic and vibrational, elastic and piezoelectric properties, where the trend towards the hexagonal monolayer (h-BeS) in the limit of large tube radius is obtained. The vibrational properties including Raman spectra and polarizabilities are evaluated via the Coupled Perturbed Hartree–Fock and Kohn–Sham (CPHF/KS) computational schemes. For the first time, the IR vibrational modes at higher tube diameter and their convergence to the h-BeS monolayer limit are reported where the vibrational and electronic contributions to both perpendicular and parallel components of polarizability tensor are additionally discussed. For the (n,0) BeS nanotube family, three ranges of IR active phonon modes are determined. The first one located in the 0–300 cm−1frequency domain, goes regularly to zero when the tube diameter increases. Both the second (300–400 cm−1) and the third (700–800 cm−1) ones tend smoothly with different slope, towards the two optical vibrational modes of the h-BeS layer. These theoretical models can be extended to investigate further issues, such as the effect caused by the addition of a dopant, the influence of the substitutional fraction of nanotube atoms and the interaction of molecules outside and/or inside of the nanotube.

A study on excited-state properties of conjugated polymers using the Pariser-Parr-Pople-Peierls model combined with configuration-interaction-singles

Singlet and triplet excited-state properties of a single poly-p-phenylenevinylene (PPV) chain are studied using the Pariser-Parr-Pople-Peierls (P-P-P-P) model combined with the configuration interaction singles (CIS) formalism. The analytic CIS energy gradient is derived using the coupled perturbed Hartree-Fock (CPHF) equations in order to perform excited-state geometry optimizations. According to whether the diagonal elements of transition density matrices being zero or not, all excited states can be classified into two types: type I with nonzero diagonal elements, and type II with zero diagonal elements. In general, type I excited states can be directly generated upon photoexcitation, and there is high probability to find the electron and the hole very close to each other. While type II excited states cannot be directly generated upon photoexcitation, and there is high probability to find the electron and the hole far to each other. Using the parameters developed for this model, we examine the energy levels, oscillator strengths, optical absorption spectrum, and optimized excited-state geometries of the excited states at low energies, and they are consistent with other theoretical work very well. This work provides a new perspective on the excited-state properties of conjugated polymers.

Is it Reasonable to Obtain Information on the Polarizability and Hyperpolarizability Only from the Electron Density?

Formulae for the static electronic polarizability and hyperpolarizability are derived in terms of moments of the ground-state electron density matrix by applying the Unsöld approximation and a generalization of the Fermi-Amaldi approximation. The latter formula for the hyperpolarizability appears to be new. The formulae manifestly transform correctly under rotations, and they are observed to be essentially cumulant expressions. Consequently, they are additive over different regions. The properties of the formula are discussed in relation to others that have been proposed in order to clarify inconsistencies. The formulae are then tested against coupled-perturbed Hartree-Fock results for a set of 40 donor-π-acceptor systems. For the polarizability, the correlation is reasonable; therefore, electron density matrix moments from theory or experiment may be used to predict polarizabilities. By constrast, the results for the hyperpolarizabilities are poor, not even within one or two orders of magnitude. The formula for the two- and three-particle density matrices obtained as a side result in this work may be interesting for density functional theories.

Partial atomic multipoles for internally consistent microelectrostatic calculations

An extension of the extant microelectrostatic methodologies, based on the concept of distributed generalized polarizability matrix derived from the Coupled Perturbed Hartree-Fock (CPHF) equations, is proposed for self-consistent calculation of charge carrier and charge-transfer (CT) state electrostatic energies in molecular solids, including the doped, defected and disordered ones. The CPHF equations are solved only once and the generalized molecular polarizability they yield enables low cost iterations that mutually adjust the molecular electronic distributions and the local electric field in which the molecules are immersed. The approach offers a precise picture of molecular charge densities, accounting for atomic partial multipoles up to order 2, which allows one to reproduce the recently reported large charge-quadrupole contributions to CT state energies in low-symmetry local environments. It is particularly well suited for repetitive calculations for large clusters (up to 300,000 atoms), and may potentially be useful for describing electrostatic solvent effects. © 2017 Wiley Periodicals, Inc.

Calculation of the atomic electric dipole moment of Pb2+ induced by nuclear Schiff moment

We report the atomic electric dipole moment induced by the P, T violating interactions in the nuclear/sub-nuclear level, for 207Pb2+ and 207Pb, owing to the recent interest in the ferroelectric crystal PbTiO3 as one of the candidates for investigating macroscopic P, T-odd effects. In this paper, we calculate the atomic electric dipole moments of 207Pb and Pb2+, parametrized in terms of the P, T-odd coupling parameter, the nuclear Schiff moment (NSM), S, in the frame-work of the coupled-perturbed Hartree–Fock theory. We estimate the Schiff moment of Pb2+ using the experimental result of a system, which is electronically similar to the Pb2+ ion. We present the dominant contributions of the electric dipole moment (EDM) matrix elements and the important correlation effects contributing to the atomic EDM of Pb2+. Our results provide the first ever calculated EDM of the Pb2+ ion, and an estimate of its NSM from which the P, T-odd energy shift in a PbTiO3 crystal can be evaluated.

New massively parallel linear-response coupled-cluster module in ACES III: application to static polarisabilities of closed-shell molecules and oligomers and of open-shell radicals

ABSTRACTStemming from our implementation of parallel coupled-cluster (CC) capabilities for electron spin resonance properties [J. Chem. Phys. 139, 174103 (2013)], we present a new massively parallel linear response CC module within ACES III. Unlike alternative parallel CC modules, this general purpose module evaluates any type of first- and second-order CC properties of both closed- and open-shell molecules employing restricted, unrestricted and restricted-open-shell Hartree–Fock (HF) references. We demonstrate the accuracy and usefulness of this module through the calculation of static polarisabilities of large molecules. Closed-shell calculations are performed at the following levels: second-order many-body perturbation theory [MBPT(2)], CC with single- and double-excitations (CCSD), coupled-perturbed HF and density functional theory (DFT), and open-shell calculations at the unrestricted CCSD (UCSSD) one. Applications involve eight closed-shell organic-chemistry molecules (Set I), the first four members of the closed-shell thiophene oligomer series (Set II), and five open-shell radicals (Set III). In Set I, all calculated average polarisabilities agree reasonably well with experimental data. In Set II, all calculated average polarisabilities vs. the number of monomers show comparable values and saturation patterns and demonstrate that experimental polarisabilities may be inaccurate. In Set III, UCCSD perpendicular polarisabilities show a reasonable agreement with previous UCCSD(T) and restricted-open-shell-MBPT(2) values.

Computation of Second Harmonic Generation for Crystalline Urea and KDP. An ab Initio Approach through the Coupled Perturbed Hartree-Fock/Kohn-Sham Scheme.

The electronic second harmonic generation (SHG) tensor, d, of crystalline urea and potassium dihydrogen phosphate (KDP) is evaluated as a function of frequency using a Gaussian type basis set and the Coupled Perturbed Hartree-Fock (CPHF) and Kohn-Sham (CPKS) schemes as implemented in the CRYSTAL code. The results of various functionals, including LDA, GGA (PBE), and global and range-separated hybrids (B3LYP, PBE0, LC-BLYP), as well as Hartree-Fock, are compared. It is found that the calculated SHG intensity always decreases as the percentage of exact exchange increases. The hybrid functionals turn out to provide results that agree well with experiment. For urea and KDP the percentage of exact exchange determined by the inverse dielectric constant is too large. At 1064 nm the vibrational contribution for urea is found to be less than 5% of the total value. To the authors' knowledge, this is the first coupled (self-consistent) calculation of SHG for any periodic system.

Communication: An efficient approach to compute state-specific nuclear gradients for a generic state-averaged multi-configuration self consistent field wavefunction

We present a new, very efficient semi-numerical approach for the computation of state-specific nuclear gradients of a generic state-averaged multi-configuration self consistent field wavefunction. Our approach eliminates the costly coupled-perturbed multi-configuration Hartree-Fock step as well as the associated integral transformation stage. The details of the implementation within the Firefly quantum chemistry package are discussed and several sample applications are given. The new approach is routinely applicable to geometry optimization of molecular systems with 1000+ basis functions using a standalone multi-core workstation.

Integration approach at the second-order perturbation theory: applications to ionization potential and electron affinity calculations.

An integration approach is developed to calculate ionization potentials (IPs), and electron affinities (EAs), which is an extension of the D-ΔMBPT(2) method [A. Beste et al., J. Chem. Phys. 2013, 138, 074101]. The latter is an extension of the single-point method of Cohen et al. [A. J. Cohen et al., J. Chem. Theory Comput. 2009, 5, 786] from the perspective of fractional charges. While relaxation effects were included only at the Hartree-Fock (HF) level in the previous methods, such effects are fully taken into account in the present method up to the second-order Møller-Plesset (MP2) level. This is made possible by deriving the full MP2 energy gradient, with respect to the orbital occupation numbers, which is solved through the coupled-perturbed HF (CP-HF) equations.

Ab Initio Calculation of the Ultraviolet-Visible (UV-vis) Absorption Spectrum, Electron-Loss Function, and Reflectivity of Solids.

The field frequency has recently been taken into account in the coupled-perturbed Hartree-Fock or Kohn-Sham method implemented in the CRYSTAL code for calculating the high-frequency dielectric constant of semiconductors up to the first electronic transitions. In this work, we document how the code has been generalized and improved in order to compute the full ultraviolet-visible (UV-vis) absorption spectrum, the electron loss function, and the reflectivity from the real and imaginary parts of the electric response property. We show how spectra are modified when the crystalline orbital relaxation due to the dynamic electric field is taken into account, and how this modification increases with the percentage of Hartree-Fock exchange in the unperturbed hybrid Hamiltonian.

Simulations of Raman Spectra Using the Fragment Molecular Orbital Method.

We developed an approach to calculate normal Raman activities based on the fragment molecular orbital method. For this purpose, we derived the FMO gradient and coupled-perturbed Hartree-Fock equations in the presence of the static electric field. The accuracy is evaluated in comparison with full ab initio calculations for a set of closed-shell and radical systems. We applied the method to calculate Raman and IR spectra of a polystyrene oligomer and crambin (PDB: 1CRN ) and performed an assignment of peaks based on localized normal modes. The computational timings demonstrate the efficiency of the method.

Theoretical investigations of optical properties of l-arginine trifluoroacetate crystal

In order to determine the molecular dipole moment (μ), polarizability (α), and first hyperpolarizability (β) of l-arginine trifluoroacetate (LATF) crystals, a series of basis sets including polarized and diffuse functions have been employed at the framework of Hartree–Fock and second order Möller–Plesset perturbation theory methods. The MP2/6-311++G(d,p) model predicts for the converged value of in-crystal dipole moment, polarizability and first hyperpolarizability are 21.2 D, 20.0 × 10−24 esu and 50.0 × 10−31 esu, respectively. The calculated HOMO and LUMO energies show that charge transfer occur within the molecule. Electronic excitation properties are discussed within the framework of the two-level model on the basis of an orbital analysis. The coupled perturbed Hartree–Fock (CPHF) procedure yields information on the dispersion behavior of first hyperpolarizability terms. The magnitudes of the various hyperpolarizability terms which describe the various second-order nonlinear processes show the following trend: β(−2ω;ω,ω) > β(0;ω,−ω) > β(0,0,0). By using the molecular structures and the molecular first hyperpolarizability, the components of second harmonic tensor coefficient d of the crystals were evaluated by the oriented-gas model.