The natural orbital functional theory (NOFT) has emerged as an alternative formalism to both density functional (DF) and wavefunction methods. In NOFT, the electronic structure is described in terms of the natural orbitals (NOs) and their occupation numbers (ONs). The approximate NOFs have proven to be more accurate than those of the density for systems with a significant multiconfigurational character, on one side, and scale better with the number of basis functions than correlated wavefunction methods, on the other side. A challenging task in NOFT is to efficiently perform orbital optimization. In this article we present DoNOF, our open source implementation based on diagonalizations that allows to obtain the resulting orbitals automatically orthogonal. The one-particle reduced-density matrix (1RDM) of the ensemble of pure-spin states provides the proper description of spin multiplets. The capabilities of the code are tested on the water molecule, namely, geometry optimization, natural and canonical representations of molecular orbitals, ionization potential, and electric moments. In DoNOF, the electron-pair-based NOFs developed in our group PNOF5, PNOF7 and PNOF7s are implemented. These JKL-only NOFs take into account most non-dynamic effects plus intrapair-dynamic electron correlation, but lack a significant part of interpair-dynamic correlation. Correlation corrections are estimated by the single-reference NOF-MP2 method that simultaneously calculates static and dynamic electron correlations taking as a reference the Slater determinant formed with the NOs of a previous PNOF calculation. The NOF-MP2 method is used to analyze the potential energy surface (PES) and the binding energy for the symmetric dissociation of the water molecule, and compare it with accurate wavefunction-based methods.
In this work, the required algebra to employ the resolution of the identity approximation within Piris Natural Orbital Functional (PNOF) is developed, leading to an implementation named DoNOF-RI. The arithmetic scaling is reduced from fifth-order to fourth-order, and the memory scaling is reduced from fourth-order to third-order, allowing significant computational time savings. After the DoNOF-RI calculation has fully converged, a restart with four-center electron repulsion integrals can be performed to remove the effect of the auxiliary basis set incompleteness, quickly converging to the exac…
AEGISS -- Atomic orbital and Entropy-based Guided Inference for Space Selection -- A novel semi-automated active space selection workflow for quantum chemistry and quantum computing applications
Algorithmiq S.r.l.（Algorithmiq有限公司）；University of L’Aquila（拉奎拉大学）；Cleveland Clinic Research（克利夫兰诊所研究）；Case Western Reserve University（凯斯西储大学）；The Abdus Salam International Centre for Theoretical Physics (ICTP)（阿卜杜斯·萨拉姆理论物理国际中心（ICTP））
In this contribution we present a protocol to evaluate partial and total Auger decay rates combining the restricted active space self-consistent field electronic structure method for the bound part of the spectrum and numerically obtained continuum orbitals in the single-channel scattering theory framework. On top of that, the two-step picture is employed to evaluate the partial rates. The performance of the method is exemplified for the prototypical Auger decay of the neon $1s^{-1}3p$ resonance. Different approximations to obtain the continuum orbitals, the partial rate matrix elements, and t…
The conventional technique for solving the equations of quantum chemistry (of solid state) is extended unconventionally to the structures possessing certain symmetries. This proposal concerns changing the way for selection of occupied orbitals, allowing, in turn, to release the unoccupied electronic states located lower than the ground state Fermi level of a specific system. Such states can be treated as 'spectral holes'. Application of this technique, in particular, when calculating the electronic structure of the HTSC-compound $YBa_2Cu_3O_{7-x}$ (0<x<1) results in the following. The spectral…
We have proposed a density-matrix renormalization group (DMRG) scheme to optimize the one-electron basis states of molecules. It improves significantly the accuracy and efficiency of the DMRG in the study of quantum chemistry or other many-fermion system with nonlocal interactions. For a water molecule, we find that the ground state energy obtained by the DMRG with only 61 optimized orbitals already reaches the accuracy of best quantum Monte Carlo calculation with 92 orbitals.
We demonstrate the use of Google's cloud-based Tensor Processing Units (TPUs) to accelerate and scale up conventional (cubic-scaling) density functional theory (DFT) calculations. Utilizing 512 TPU cores, we accomplish the largest such DFT computation to date, with 247848 orbitals, corresponding to a cluster of 10327 water molecules with 103270 electrons, all treated explicitly. Our work thus paves the way towards accessible and systematic use of conventional DFT, free of any system-specific constraints, at unprecedented scales.
In quantum chemistry, one of the most important challenges is the static correlation problem when solving the electronic Schrödinger equation for molecules in the Born--Oppenheimer approximation. In this article, we analyze the tailored coupled-cluster method (TCC), one particular and promising method for treating molecular electronic-structure problems with static correlation. The TCC method combines the single-reference coupled-cluster (CC) approach with an approximate reference calculation in a subspace [complete active space (CAS)] of the considered Hilbert space that covers the static cor…
Molecular orbitals based on the linear combination of Gaussian type orbitals are arguably the most employed discretization in quantum chemistry simulations, both on quantum and classical devices. To circumvent a potentially dense two-body interaction tensor and obtain lower asymptotic costs for quantum simulations of chemistry, the discontinuous Galerkin (DG) procedure using a rectangular partitioning strategy was recently piloted [McClean et al, New J. Phys. 22, 093015, 2020]. The DG approach interpolates in a controllable way between a compact description of the two-body interaction tensor t…
In this article, we present an emerging field of quantum chemistry at finite temperature. We discuss its recent developments on both theoretical and experimental fronts.We describe and analyze several experimental investigations related to the temperature effects on the structure, electronic spectra,or bond rupture forces for molecules. This includes the study of the temperature impact on the pathway shifts for the protein unfolding by atomic force microscopy, the temperature dependence of the absorption spectra of electrons in solvents, and temperature influence over the intermolecular forces…
In this work we present an interpretation of experimental O K-edge x-ray absorption near edge structure (XANES) in perovskite-type WO3 and AWO3 compounds (A = H and Na) using three different first principles approaches: (i) full-multiple-scattering (FMS) formalism (the real-space FEFF code), (ii) hybrid density functional theory (DFT) method with partial incorporation of exact Hartree-Fock exchange using formalism of the linear combination of atomic orbitals (LCAO) as implemented in the CRYSTAL code; (iii) plane-wave DFT method using formalism of the projector-augmented waves (PAW) as implemen…
Applications of quantum simulation algorithms to obtain electronic energies of molecules on noisy intermediate-scale quantum (NISQ) devices require careful consideration of resources describing the complex electron correlation effects. In modeling second-quantized problems, the biggest challenge confronted is that the number of qubits scales linearly with the size of molecular basis. This poses a significant limitation on the size of the basis sets and the number of correlated electrons included in quantum simulations of chemical processes. To address this issue and to enable more realistic si…
The emergence of machine learning methods in quantum chemistry provides new methods to revisit an old problem: Can the predictive accuracy of electronic structure calculations be decoupled from their numerical bottlenecks? Previous attempts to answer this question have, among other methods, given rise to semi-empirical quantum chemistry in minimal basis representation. We present an adaptation of the recently proposed SchNet for Orbitals (SchNOrb) deep convolutional neural network model [Nature Commun. 10, 5024 (2019)] for electronic wave functions in an optimised quasi-atomic minimal basis re…
We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a…
InstaDeep（英斯塔迪普）；University of Oxford（牛津大学）；Russian Quantum Center（俄罗斯量子中心）
In recent years, neural network quantum states (NNQS) have emerged as powerful tools for the study of quantum many-body systems. Electronic structure calculations are one such canonical many-body problem that have attracted significant research efforts spanning multiple decades, whilst only recently being attempted with NNQS. However, the complex non-local interactions and high sample complexity are significant challenges that call for bespoke solutions. Here, we parameterise the electronic wavefunction with a novel autoregressive neural network (ARN) that permits highly efficient and scalable…
