Related papers: One-Center Nonrelativistic Integrals of Second Ord…
We introduce an alternative approach to the first-principles calculation of NMR shielding tensors. These are obtained from the derivative of the orbital magnetization with respect to the application of a microscopic, localized magnetic…
We report an implementation of the nuclear magnetic resonance (NMR) shielding ($\sigma$), isotope-independent indirect spin-spin coupling ($K$) and the magnetizability ($\xi$) tensors in the frozen density embedding (FDE) scheme using the…
Using the shift-operator technique, a compact formula for the Fourier transform of a product of two Slater-type orbitals located on different atomic centers is derived. The result is valid for arbitrary quantum numbers and was found to be…
Three-centre nuclear attraction integrals, which arise in density functional and \textit{ab initio} calculations, are one of the most time-consuming computations involved in molecular electronic structure calculations. Even for relatively…
The auxiliary functions provide efficient computation of integrals arising at the self-consistent field (SCF) level for molecules using Slater-type bases. This applies both in relativistic and non-relativistic electronic structure theory.…
The Slater-type orbital basis with non-integer principal quantum numbers is a physically and mathematically motivated choice for molecular electronic structure calculations in both non-relativistic and relativistic theory. The…
Ab initio QED calculations of the nuclear magnetic shielding constant in helium-like ions are presented. We combine the nonrelativistic QED approach based on an expansion in powers of the fine-structure constant $\alpha$ and the so-called…
The main aim of this paper is to develop a framelet representation of the tensor nuclear norm for third-order tensor completion. In the literature, the tensor nuclear norm can be computed by using tensor singular value decomposition based…
We perform a recursive reduction of one-loop $n$-point rank $R$ tensor Feynman integrals [in short: $(n,R)$-integrals] for $n\leq 6$ with $R\leq n$ by representing $(n,R)$-integrals in terms of $(n,R-1)$- and $(n-1,R-1)$-integrals. We use…
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…
The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and providing reconstruction formulas for them. These tensors…
In any ab initio molecular orbital (MO) calculations, the major task involves the computation of the so-called molecular multi-center integrals. Multi-center integral calculations is a very challenging mathematical problem in nature.…
Within the lowest-order relativistic approximation ($\sim v^2/c^2$) and to first order in $m_e/M$, the tensorial form of the relativistic corrections of the nuclear recoil Hamiltonian is derived, opening interesting perspectives for…
A simple method is outlined for analytic evaluation of the basic 2-electron atomic integral with integrand containing products of atomic s-type Slater orbitals and exponentially correlated function of the form $r_{ij}…
We describe an accurate and scalable implementation for the computation of molecular nuclear magnetic resonance shieldings, J-couplings, and magnetizabilities within nonrelativistic semilocal density functional theory, based on numeric…
We present a benchmark of the density functional linear response calculation of NMR shieldings within the Gauge-Including Projector-Augmented-Wave method against all-electron Augmented-Plane-Wave$+$local-orbital and uncontracted Gaussian…
Standard numerical integrators suffer from an order reduction when applied to nonlinear Schr\"{o}dinger equations with low-regularity initial data. For example, standard Strang splitting requires the boundedness of the solution in $H^{r+4}$…
We consider rank-one non-symmetric tensor estimation and derive simple formulas for the mutual information. We start by the order 2 problem, namely matrix factorization. We treat it completely in a simpler fashion than previous proofs using…
We present a theory of nuclear magnetic resonance (NMR) shielding tensors for electronic states with arbitrary degeneracy. The shieldings are here expressed in terms of generalized Zeeman ($g^{(k)}$) and hyperfine ($A^{(k)}$) tensors, of…
We present a theory for the temperature-dependent nuclear magnetic shielding tensor of molecules with arbitrary electronic structure. The theory is a generalization of Ramsey's theory for closed-shell molecules. The shielding tensor is…