Linear-Scaling Implementation of Multilevel Hartree-Fock Theory.
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ABSTRACT:
SUBMITTER: Goletto L
PROVIDER: S-EPMC8675138 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:In this work we present the particle-breaking Hartree-Fock (PBHF) model which is a mean-field approach to open molecular systems. The interaction of a system with the environment is parametrized through a particle-breaking term in the molecular Hamiltonian. The PBHF wave function is constructed through an exponential unitary transformation of a Slater determinant with a given number of electrons. We consider only the closed-shell formalism. The parametrization results in a linear combination of Slater determinants with different numbers of electrons, i.e., the PBHF wave function is not an eigenfunction of the number operator. As a result, the density matrix may have fractional occupations which are, because of the unitary parametrization, always between 0.0 and 2.0. The occupations are optimized simultaneously with the orbitals, using the trust-region optimization procedure. In the limit of a particle-conserving Hamiltonian, the PBHF optimization will converge to a standard Hartree-Fock wave function. We show that the average number of electrons may be decreased or increased depending on whether the particle-breaking term affects occupied or virtual orbitals.
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Project description:The ability to perform ab initio electronic structure calculations that scales linearly with the system size is one of the central aims in theoretical chemistry. In this study, the implementation of the divide-and-conquer (DC) algorithm, an algorithm with the potential to aid the achievement of true linear scaling within Hartree-Fock (HF) theory is revisited. Standard HF calculations solve the Roothaan-Hall equations for the whole system; in the DC-HF approach, the diagonalization of the Fock matrix is carried out on smaller subsystems. The DC algorithm for HF calculations was validated on polyglycines, polyalanines and eleven real three-dimensional proteins of up to 608 atoms in this work. We also found that a fragment-based initial guess using molecular fractionation with conjugated caps (MFCC) method significantly reduces the number of SCF cycles and even is capable of achieving convergence for some globular proteins where the simple superposition of atomic densities (SAD) initial guess fails.
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Project description:The X-ray constrained wavefunction (XC-WF) method proposed by Jayatilaka [Jayatilaka & Grimwood (2001) ▸, Acta Cryst. A57, 76-86] has attracted much attention because it represents a possible third way of theoretically studying the electronic structure of atoms and molecules, combining features of the more popular wavefunction- and DFT-based approaches. In its original formulation, the XC-WF technique extracts statistically plausible wavefunctions from experimental X-ray diffraction data of molecular crystals. A weight is used to constrain the pure Hartree-Fock solution to the observed X-ray structure factors. Despite the wavefunction being a single Slater determinant, it is generally assumed that its flexibility could guarantee the capture, better than any other experimental model, of electron correlation effects, absent in the Hartree-Fock Hamiltonian but present in the structure factors measured experimentally. However, although the approach has been known for long time, careful testing of this fundamental hypothesis is still missing. Since a formal demonstration is impossible, the validation can only be done heuristically and, to accomplish this task, X-ray constrained Hartree-Fock calculations have been performed using structure factor amplitudes computed at a very high correlation level (coupled cluster) for selected molecules in isolation, in order to avoid the perturbations due to intermolecular interactions. The results show that a single-determinant XC-WF is able to capture the electron correlation effects only partially. The largest amount of electron correlation is extracted when: (i) a large external weight is used (much larger than what has normally been used in XC-WF calculations using experimental data); and (ii) the high-order reflections, which carry less information on the electron correlation, are down-weighted (or even excluded), otherwise they would bias the fitting towards the unconstrained Hartree-Fock wavefunction.
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Project description:Quantum computers hold promise to circumvent the limitations of conventional computing for difficult molecular problems. However, the accumulation of quantum logic errors on real devices represents a major challenge, particularly in the pursuit of chemical accuracy requiring the inclusion of electronic correlation effects. In this work we implement the quantum computed moments (QCM) approach for hydrogen chain molecular systems up to H[Formula: see text]. On a superconducting quantum processor, Hamiltonian moments, [Formula: see text] are computed with respect to the Hartree-Fock state, which are then employed in Lanczos expansion theory to determine an estimate for the ground-state energy which incorporates electronic correlations and manifestly improves on the direct energy measurement. Post-processing purification of the raw QCM data takes the estimate below the Hartree-Fock energy to within 99.9% of the exact electronic ground-state energy for the largest system studied, H[Formula: see text]. Calculated dissociation curves indicate precision at about 10mH for this system and as low as 0.1mH for molecular hydrogen, H[Formula: see text], over a range of bond lengths. In the context of stringent precision requirements for chemical problems, these results provide strong evidence for the error suppression capability of the QCM method, particularly when coupled with post-processing error mitigation. While calculations based on the Hartree-Fock state are tractable to classical computation, these results represent a first step towards implementing the QCM method in a quantum chemical trial circuit. Greater emphasis on more efficient representations of the Hamiltonian and classical preprocessing steps may enable the solution of larger systems on near-term quantum processors.
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Project description:Automatic differentiation (AD) is a powerful tool that allows calculating derivatives of implemented algorithms with respect to all of their parameters up to machine precision, without the need to explicitly add any additional functions. Thus, AD has great potential in quantum chemistry, where gradients are omnipresent but also difficult to obtain, and researchers typically spend a considerable amount of time finding suitable analytical forms when implementing derivatives. Here, we demonstrate that AD can be used to compute gradients with respect to any parameter throughout a complete quantum chemistry method. We present DiffiQult, a Hartree-Fock implementation, entirely differentiated with the use of AD tools. DiffiQult is a software package written in plain Python with minimal deviation from standard code which illustrates the capability of AD to save human effort and time in implementations of exact gradients in quantum chemistry. We leverage the obtained gradients to optimize the parameters of one-particle basis sets in the context of the floating Gaussian framework.
| S-EPMC5968443 | biostudies-literature
Project description:Linear-scaling density functional theory (DFT) is an efficient method to describe the electronic structures of molecules, semiconductors, and insulators to avoid the high cubic-scaling cost in conventional DFT calculations. Here, we present a parallel implementation of linear-scaling density matrix trace correcting (TC) purification algorithm to solve the Kohn-Sham (KS) equations with the numerical atomic orbitals in the HONPAS package. Such a linear-scaling density matrix purification algorithm is based on the Kohn's nearsightedness principle, resulting in a sparse Hamiltonian matrix with localized basis sets in the DFT calculations. Therefore, sparse matrix multiplication is the most time-consuming step in the density matrix purification algorithm for linear-scaling DFT calculations. We propose to use the MPI_Allgather function for parallel programming to deal with the sparse matrix multiplication within the compressed sparse row (CSR) format, which can scale up to hundreds of processing cores on modern heterogeneous supercomputers. We demonstrate the computational accuracy and efficiency of this parallel density matrix purification algorithm by performing large-scale DFT calculations on boron nitrogen nanotubes containing tens of thousands of atoms.
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Project description:The counterpoise (CP) correction by Boys and Bernardi has been well accepted as a reliable strategy to account for basis set superposition error (BSSE) in intermolecular complexes. The behavior of the CP correction was thoroughly studied in individual molecules of molecular complexes. This work studies the performance of the CP correction in many-body clusters including three-body clusters of organic compounds in the 3B-69 dataset. Additionally, we used crystal structures of polymorphs of benzene, aspirin, and oxalyl dihydrazide (ODH) to construct a many-body cluster dataset, abbreviated as the MBC-36 dataset, consisting of two, four and eight molecules, and 16 molecules in the case of benzene. A series of Dunning's basis sets-cc-pXZ and aug-cc-pXZ (X = D and T)-were used to predict CP-corrected Hartree-Fock (HF) interaction energies of the 3B-69 and MBC-36 datasets. The CP-corrected interaction energies were found to be basis-set independent, whereas the non-CP corrected interaction energies were found not to a follow a smooth exponential fitting as previously found for electronic energies of individual molecules. This observation was attributed to the presence of non-additive induction forces in some clusters. Two 2 × 2 × 2 supercells of benzene polymorphs were constructed to explore the local nature of BSSE effects. A cut-off radius of 10 Å was demonstrated to be sufficient to fully recover these effects. Although the behavior of CP correction was found to be non-conventional in many-body clusters of organic compounds, the use of a small basis set such as cc-pVDZ showed excellent performance in the prediction of HF interaction energies.
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Project description:The coupled-cluster (CC) singles and doubles with perturbative triples [CCSD(T)] method is frequently referred to as the "gold standard" of modern computational chemistry. However, the high computational cost of CCSD(T) [O(N7)], where N is the number of basis functions, limits its applications to small-sized chemical systems. To address this problem, efficient implementations of linear-scaling coupled-cluster methods, which employ the systematic molecular fragmentation (SMF) approach, are reported. In this study, we aim to do the following: (1) To achieve exact linear scaling and to obtain a pure ab initio approach, we revise the handling of nonbonded interactions in the SMF approach, denoted by LSSMF. (2) A new fragmentation algorithm, which yields smaller-sized fragments, that better fits high-level CC methods is introduced. (3) A modified nonbonded fragmentation scheme is proposed to enhance the existent algorithm. Performances of the LSSMF-CC approaches, such as LSSMF-CCSD(T), are compared with their canonical versions for a set of alkane molecules, CnH2n+2 (n = 6-10), which includes 142 molecules. Our results demonstrate that the LSSMF approach introduces negligible errors compared with the canonical methods; mean absolute errors (MAEs) are between 0.20 and 0.59 kcal mol-1 for LSSMF(3,1)-CCSD(T). For a larger alkanes set (L12), CnH2n+2 (n = 50-70), the performance of LSSMF for the second-order perturbation theory (MP2) is investigated. For the L12 set, various bonded and nonbonded levels are considered. Our results demonstrate that the combination of bonded level 6 with nonbonded level 2, LSSMF(6,2), provides very accurate results for the MP2 method with a MAE value of 0.32 kcal mol-1. The LSSMF(6,2) approach yields more than a 26-fold reduction in errors compared with LSSMF(3,1). Hence, we obtain substantial improvements over the original SMF approach. To illustrate the efficiency and applicability of the LSSMF-CCSD(T) approach, we consider an alkane molecule with 10,004 atoms. For this molecule, the LSSMF(3,1)-CCSD(T)/cc-pVTZ energy computation, on a Linux cluster with 100 nodes, 4 cores, and 5 GB of memory provided to each node, is performed just in ∼24 h. As a second test, we consider a biomolecular complex (PDB code: 1GLA), which includes 10,488 atoms, to assess the efficiency of the LSSMF approach. The LSSMF(3,1)-FNO-CCSD(T)/cc-pVTZ energy computation is completed in ∼7 days for the biomolecular complex. Hence, our results demonstrate that the LSSMF-CC approaches are very efficient. Overall, we conclude the following: (1) The LSSMF(m, n)-CCSD(T) methods can be reliably used for large-scale chemical systems, where the canonical methods are not computationally affordable. (2) The accuracy of bonded level 3 is not satisfactory for large chemical systems. (3) For high-accuracy studies, bonded level 5 (or higher) and nonbonded level 2 should be employed.
| S-EPMC9476663 | biostudies-literature
Project description:ObjectiveThe present study aims to establish the relationship between the reported radical-scavenging activities of flavonoids and some enthalpy changes that may occur during flavonoids' reactions with free radicals.MethodEight flavonoids were chosen for the study on the basis of their structural merits and reported 1,1-diphenyl-2-picryl-hydrazyl scavenging activities. Enthalpy changes accompanying interconversions between selected conformations (including spin multiplicities) and homolytic dissociations were estimated.ResultsA novel relationship exists between the total enthalpy of reaction for the abstraction of two hydrogen atoms from flavonoids, their reported radical-scavenging activities and the enthalpy of the homolytic dissociation of hydrogen molecule (104.206 kcal mol(-1)). Only those flavonoids which could give up two hydrogen atoms with total enthalpy changes well below 104.206 kcal mol(-1) were active radical scavengers.DiscussionBy appealing to equilibrium dynamics, we demonstrated that, for flavonoids to be able to donate hydrogen atoms, the change in enthalpy accompanying the abstraction of two hydrogen atoms needs to be less than 104.206 kcal mol(-1). This condition does not seem to be restricted to flavonoids only but rather generally applicable to chian-breaking antioxidants.ConclusionThermodynamical relationships may be the most important factors governing the radical-scavenging reactions of flavonoids and possibly other compounds as well. Nevertheless, a more complete characterization of antioxidants would necessitate kinetic analysis.
| S-EPMC6837546 | biostudies-literature
Project description:The full configuration interaction (full-CI) method is capable of providing the numerically best wave functions and energies of atoms and molecules within basis sets being used, although it is intractable for classical computers. Quantum computers can perform full-CI calculations in polynomial time against the system size by adopting a quantum phase estimation algorithm (QPEA). In the QPEA, the preparation of initial guess wave functions having sufficiently large overlap with the exact wave function is recommended. The Hartree-Fock (HF) wave function is a good initial guess only for closed shell singlet molecules and high-spin molecules carrying no spin-? unpaired electrons, around their equilibrium geometry, and thus, the construction of multiconfigurational wave functions without performing post-HF calculations on classical computers is highly desired for applying the method to a wide variety of chemistries and physics. In this work, we propose a method to construct multiconfigurational initial guess wave functions suitable for QPEA-based full-CI calculations on quantum computers, by utilizing diradical characters computed from spin-projected UHF wave functions. The proposed approach drastically improves the wave function overlap, particularly in molecules with intermediate diradical characters.
| S-EPMC6346626 | biostudies-literature