15,336 research outputs found
Explicitly correlated Gaussian functions with shifted-center and projection techniques in pre-Born-Oppenheimer calculations
Numerical projection methods are elaborated for the calculation of
eigenstates of the non-relativistic many-particle Coulomb Hamiltonian with
selected rotational and parity quantum numbers employing shifted explicitly
correlated Gaussian functions, which are, in general, not eigenfunctions of the
total angular momentum and parity operators. The increased computational cost
of numerically projecting the basis functions onto the irreducible
representations of the three dimensional rotation-inversion group is the price
to pay for the increased flexibility of the basis functions. This increased
flexibility allowed us to achieve a substantial improvement for the variational
upper bound to the Pauli-allowed ground-state energy of the
Hpppee molecular ion treated as an explicit
five-particle system. We compare our pre-Born-Oppenheimer result for this
molecular ion with rovibrational results including non-adiabatic corrections.Comment: 29 pages, 3 figures, 4 table
Fast evaluation of solid harmonic Gaussian integrals for local resolution-of-the-identity methods and range-separated hybrid functionals
An integral scheme for the efficient evaluation of two-center integrals over
contracted solid harmonic Gaussian functions is presented. Integral expressions
are derived for local operators that depend on the position vector of one of
the two Gaussian centers. These expressions are then used to derive the formula
for three-index overlap integrals where two of the three Gaussians are located
at the same center. The efficient evaluation of the latter is essential for
local resolution-of-the-identity techniques that employ an overlap metric. We
compare the performance of our integral scheme to the widely used Cartesian
Gaussian-based method of Obara and Saika (OS). Non-local interaction potentials
such as standard Coulomb, modified Coulomb and Gaussian-type operators, that
occur in range-separated hybrid functionals, are also included in the
performance tests. The speed-up with respect to the OS scheme is up to three
orders of magnitude for both, integrals and their derivatives. In particular,
our method is increasingly efficient for large angular momenta and highly
contracted basis sets.Comment: 18 pages, 2 figures; accepted manuscript. v2: supplementary material
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Generalized elimination of the global translation from explicitly correlated Gaussian functions
This paper presents the multi-channel generalization of the center-of-mass
kinetic energy elimination approach [Mol. Phys., 111 2086 (2013)] when the
Schr\"odinger equation is solved variationally with explicitly correlated
Gaussian functions. The approach has immediate relevance in many-particle
systems which are handled without the Born--Oppenheimer approximation and can
be employed also for Dirac-type Hamiltonians. The practical realization and
numerical properties of solving the Schr\"odinger equation in laboratory-frame
Cartesian coordinates are demonstrated for the ground rovibronic state of the
H ion and the
H molecule.Comment: 24 pages, 1 figure, 2 table
The genesis of the quantum theory of the chemical bond
An historical overview is given of the relevant steps that allowed the
genesis of the quantum theory of the chemical bond, starting from the
appearance of the new quantum mechanics and following later developments till
approximately 1931. General ideas and some important details are discussed
concerning molecular spectroscopy, as well as quantum computations for simple
molecular systems performed within perturbative and variational approaches, for
which the Born-Oppenheimer method provided a quantitative theory accounting for
rotational, vibrational and electronic states. The novel concepts introduced by
the Heitler-London theory, complemented by those underlying the method of the
molecular orbitals, are critically analyzed along with some of their relevant
applications. Further improvements in the understanding of the nature of the
chemical bond are also considered, including the ideas of one-electron and
three-electron bonds introduced by Pauling, as well as the generalizations of
the Heitler-London theory firstly performed by Majorana, which allowed the
presence of ionic structures into homopolar compounds and provided the
theoretical proof of the stability of the helium molecular ion. The study of
intermolecular interactions, as developed by London, is finally examined.Comment: amsart, 34 pages, 2 figure
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