Related papers: Fundamentals of Molecular Integrals Evaluation
In previous work, the necessary integrals arising from correlated wavefunctions were expressed in forms suitable for numerical integration. For the evaluation of $r_{12}$ and $1/r_{12}$ integrals an analytic formula is derived.…
We present explicit expressions for multi-fold logarithmic integrals that are equivalent to sums over polygamma functions at integer argument. Such relations find application in perturbative quantum field theory, quantum chemistry, analytic…
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…
We introduce an original approach to geometric calculus in which we define derivatives and integrals on functions which depend on extended bodies in space--that is, paths, surfaces, and volumes etc. Though this theory remains to be fully…
Gaussian building blocks are essential for photonic quantum information processing, and universality can be practically achieved by equipping Gaussian circuits with adaptive measurement and feedforward. The number of adaptive steps then…
In recent years, there has been considerable interest in developing machine learning models on graphs to account for topological inductive biases. In particular, recent attention has been given to Gaussian processes on such structures since…
Advantages of introducing the electron structure function in electron induced processes are demonstrated. At present energies the same experiment gives more precise description of the electron than photon structure. The momentum scales…
The ionization by photon or electron impact of the inner (2a1) and outer (1t2) valence orbitals of the CH4 molecule is investigated theoretically. In spite of a number of approximations, including a monocentric approach and a rather simple…
In order to understand the physics phenomea on the fundamental aspects, the software simulations are a good exercise to succed in this way. Some work of heat transport and molecular physics laboratory are studied in a comparative mode…
We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
A new iterative solver is proposed to efficiently calculate the ground state electronic structure in Density Functional Theory calculations. This algorithm is particularly useful for simulating physical systems considered difficult to…
These lecture notes provide a self-contained introduction to Euler integrals, which are frequently encountered in applications. In particle physics, they arise as Feynman integrals or string amplitudes. Our four selected topics demonstrate…
Exposing a molecule to intense light pulses may bring this molecule to a nonstationary quantum state, thus launching correlated dynamics of electronic and nuclear subsystems. Although much had been achieved in the understanding of…
An operatorial method, already employed to formulate a generalization of the Ramanujan master theorem, is applied to the evaluation of integrals of various type. This technique provide a very flexible and powerful tool yielding new results…
Machine Learning Interatomic Potentials play a fundamental role in computational chemistry and materials science, enabling applications from molecular dynamics simulations to drug design and materials discovery. While recent approaches can…
This talk presents foundations of mathematics as a historically variable set of principles appealing to various modes of human intuition and devoid of any prescriptive/prohibitive power. At each turn of history, foundations crystallize the…
Molecular Dynamics simulations are becoming a powerful tool for examining and predicting atomic and molecular processes in various environment. The present review shows how, in the fields of plasma physics, chemistry and interactions with…
An analytically derived 'integral operator' approach is introduced to estimate the expectation value of a quantum operator for an evolving state weighted with an exponential function. This allows to compute quantities useful in Nuclear…
We describe the fundamental equations for description of electron-photon interactions in insulating nanostructures. Since the theory for the nanostructures are based on the theory for the bulk crystals, we shall describe elements of the…
Machine learning holds the promise of learning the energy functional via examples, bypassing the need to solve complicated quantum-chemical equations and realizing efficient computing of molecular electronic properties.