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Register a new userNMR Chemical Shift Computations at Second-Order M{o}ller-Plesset Perturbation Theory Using Gauge-Including Atomic Orbitals and Cholesky-Decomposed Two-Electron Integrals
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We report on a formulation and implementation of a scheme to compute NMR shieldings at second-order Moller-Plesset (MP2) perturbation theory using gauge-including atomic orbitals (GIAOs) to ensure gauge-origin independence and Cholesky decomposition (CD) to handle unperturbed as well as perturbed two-electron integrals. We investigate the accuracy of the CD for the derivatives of the two-electron integrals with respect to an external magnetic field as well as for the computed NMR shieldings, before we illustrate the applicability of our CD based GIAO-MP2 scheme in calculations involving up to about one hundred atoms and more than one thousand basis functions.
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In quantum chemistry, obtaining a systems mean-field solution and incorporating electron correlation in a post Hartree-Fock (HF) manner comprise one of the standard protocols for ground-state calculations. In principle, this scheme can also describe excited states but is not widely used at present, primarily due to the difficulty of locating the mean-field excited states. With recent developments in excited-state orbital relaxation, self-consistent excited-state solutions can now be located routinely at various levels of theory. In this work, we explore the possibility of correcting HF excited states using M{o}ller-Plesset perturbation theory to the second order. Among various PT2 variants, we find that the restricted open-shell MP2 (ROMP2) gives excitation energies comparable to the best density functional theory results, delivering $sim 0.2$ eV mean unsigned error over a wide range of single-configuration state function excitations, at only non-iterative $O(N^5)$ computational scaling.
The calculation of the MP2 correlation energy for extended systems can be viewed as a multi-dimensional integral in the thermodynamic limit, and the standard method for evaluating the MP2 energy can be viewed as a trapezoidal quadrature scheme. We demonstrate that existing analysis neglects certain contributions due to the non-smoothness of the integrand, and may significantly underestimate finite-size errors. We propose a new staggered mesh method, which uses two staggered Monkhorst-Pack meshes for occupied and virtual orbitals, respectively, to compute the MP2 energy. The staggered mesh method circumvents a significant error source in the standard method, in which certain quadrature nodes are always placed on points where the integrand is discontinuous. One significant advantage of the proposed method is that there are no tunable parameters, and the additional numerical effort needed can be negligible compared to the standard MP2 calculation. Numerical results indicate that the staggered mesh method can be particularly advantageous for quasi-1D systems, as well as quasi-2D and 3D systems with certain symmetries.
Despite decades of practice, finite-size errors in many widely used electronic structure theories for periodic systems remain poorly understood. For periodic systems using a general Monkhorst-Pack grid, there has been no rigorous analysis of the finite-size error in the Hartree-Fock theory (HF) and the second order M{o}ller-Plesset perturbation theory (MP2), which are the simplest wavefunction based method, and the simplest post-Hartree-Fock method, respectively. Such calculations can be viewed as a multi-dimensional integral discretized with certain trapezoidal rules. Due to the Coulomb singularity, the integrand has many points of discontinuity in general, and standard error analysis based on the Euler-Maclaurin formula gives overly pessimistic results. The lack of analytic understanding of finite-size errors also impedes the development of effective finite-size correction schemes. We propose a unified method to obtain sharp convergence rates of finite-size errors for the periodic HF and MP2 theories. Our main technical advancement is a generalization of the result of [Lyness, 1976] for obtaining sharp convergence rates of the trapezoidal rule for a class of non-smooth integrands. Our result is applicable to three-dimensional bulk systems as well as low dimensional systems (such as nanowires and 2D materials). Our unified analysis also allows us to prove the effectiveness of the Madelung-constant correction to the Fock exchange energy, and the effectiveness of a recently proposed staggered mesh method for periodic MP2 calculations [Xing, Li, Lin, 2021]. Our analysis connects the effectiveness of the staggered mesh method with integrands with removable singularities, and suggests a new staggered mesh method for reducing finite-size errors of periodic HF calculations.
Approximate natural orbitals are investigated as a way to improve a Monte Carlo configuration interaction (MCCI) calculation. We introduce a way to approximate the natural orbitals in MCCI and test these and approximate natural orbitals from MP2 and QCISD in MCCI calculations of single-point energies. The efficiency and accuracy of approximate natural orbitals in MCCI potential curve calculations for the double hydrogen dissociation of water, the dissociation of carbon monoxide and the dissociation of the nitrogen molecule are then considered in comparison with standard MCCI when using full configuration interaction as a benchmark. We also use the method to produce a potential curve for water in an aug-cc-pVTZ basis. A new way to quantify the accuracy of a potential curve is put forward that takes into account all of the points and that the curve can be shifted by a constant. We adapt a second-order perturbation scheme to work with MCCI (MCCIPT2) and improve the efficiency of the removal of duplicate states in the method. MCCIPT2 is tested in the calculation of a potential curve for the dissociation of nitrogen using both Slater determinants and configuration state functions.
The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can be useful in the study of different quantum mechanical problems in both the theory and practice of calculations dealing with atoms, molecules, nuclei and solids when the integer and noninteger n complex and real atomic orbitals basis sets are emploed. This work presented the development of our previous paper (I.I. Guseinov, Phys. Rev. A, 32 (1985) 1864).
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