On the use of explicitly correlated functions in variational computations for small molecules

Rychlewski, Jacek

doi:10.1002/qua.560490412

Cited by 27 publications

(9 citation statements)

References 91 publications

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“…Such a new scaled wave function 6 +"= V +(Vri Vr»mrs W4) (12) (v) 2(T) (13) where (V) and (T) are the expectation values of the potential and kinetic energy operators, respectively. The exact wave function describing a stable state of an atom has y= 1 (2) tensive optimization the wave functions have the scaling factors so close to one that the scaling brings practically no further energy lowering.…”

Section: Resultsmentioning

confidence: 99%

“…During the last decade, the energy error was decreased to a fraction of cm ' [4,9,10] to reach finally the level of accuracy that has never been obtained before for any molecular system [11].A possibility of obtaining results of the same quality for HeH+ and H&+ has also been presented [4,10,12]. Application of the ECG to three-electron systems also results in high accuracy as has been shown for Li [13] and H& [10,14].…”

Section: Introductionmentioning

confidence: 96%

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Explicitly correlated Gaussian functions in variational calculations: The ground state of the beryllium atom

1995

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Explicitly correlated Gaussian functions are applied to extensive variational calculations of the 'S ground state of the beryllium atom. The convergence of the energy with respect to the basis-set expansion length is investigated. The nonrelativistic clamped-nuclei energy computed from a 1200-term wave function equals -14.667 355 hartree and is in error by about 1 cm '. This is the lowest variational upper bound to the beryllium ground-state energy reported to date and it shows that recent empirical estimates of the nonrelativistic energy of the Be atom lie slightly too high. Several expectation values, including powers of interparticle distances and the Dirac 6 function, are computed. The nuclear magnetic shielding constant, the magnetic susceptibility, the specific mass shifts, the transition isotope shift, and the electron density at the nucleus position are evaluated.PACS number(s): 31.15. Ar, 31.25.v

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Explicitly correlated Gaussian functions in variational calculations: The ground state of the beryllium atom

1995

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“…For a molecule the interaction of the magnetic moment o f a n ucleus, N (2) where (00) stands for the zero-order function, which is obtained by solving the standard electronic Schrodinger equation.…”

Section: Methodsmentioning

confidence: 99%

“…Moreover the hydrogen molecule is easily accessible experimentally. Recently a new and very e ective method for variational quantum computations for many-electron systems was introduced 1,2,3,4]. In this method exponentially correlated gaussian functions are employed as basis functions.…”

Section: Introductionmentioning

confidence: 99%

The nuclear magnetic shielding and spin-rotation constants of the hydrogen molecule

Komasa

Rychlewski

Raynes

1995

Chemical Physics Letters

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The variation-perturbation method, employing an explicitly correlated basis set in the form of gaussian functions with exponential correlation factors, has been used to calculate the paramagnetic component o f t h e n uclear magnetic shielding and electronic contribution to the spin-rotation constant f o r t h e h ydrogen molecule in its ground state. The diamagnetic components of the shielding tensor have also been computed. The computations have been performed for three internuclear distances in the vicinity of equilibrium. A comparison of the calculated quantities, which are of great accuracy, with the experimental data reveals a small but signi cant discrepancy between theory and experiment.

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“…It becomes clear that without clever and efficiently programmed algorithms our method would be hopelessly time-consuming. (8) (9) (10) where the sequence is defined by the recurrence relation and c 0 is an arbitrary starting vector. It can be proven [6] that converges to an eigenvector corresponding to this eigenvalue which is closest to the constant Therefore, the eigenvalue (energy) has to be known approximately at the beginning.…”

Section: Inverse Iteration Theorymentioning

confidence: 99%

The Role of Efficient Programming in Theoretical Chemistry and Physics Problems

Cencek¹

1996

CMST

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Various aspects of efficient programming of high-performance computer systems are discussed, using an example from modern electronic structure theory. It is shown that efficient programming is indispensable in today's theoretical studies by reducing drastically involved computer time. Timings from our quantum chemical program CORREL are given for several platforms ranging from Cray Y-MP EL to PC/486. Introduction Variational method in quantum mechanicsThe quantum world is one of these fields where physics and chemistry meet particularly often. As it is commonly known, elementary particles and sufficiently small objects built out of them-such as atoms and molecules-cannot be described in terms of classical Newton mechanics, even when we neglect relativistic effects contained in Einstein's theory. Instead of Newton's laws we have to deal with the famous Schroedinger equation 7(1) where is the so-called Hamilton operator modifying in some defined way the function following it. The construction of this operator for a given quantum system is usually a simple task. To solve the Schroedinger equation means to find both the "wavefunction", and the total energy of the system, E. As follows from quantum mechanics, if we know we can easily calculate, apart from the energy, all static properties of the system.Unfortunately, from what the chemist may be interested in, namely atoms and molecules, only trivial one-electron cases such as the hydrogen atom can be directly solved. For larger systems the Schroedinger equation becomes so difficult that one is forced to look for some approximations. One commonly used, called the Born-Oppenheimer approximation, treats the movement of the electrons independently of this of the nuclei, basing upon the significant difference between masses of the two types of particles. In the first step, the electronic Schrödinger equation is solved, i.e. it is assumed that the nuclear masses in the Hamilton operator are infinite (the nuclei do not move) and the function depends only on the electronic coordinates. This is the subject of the electronic structure theory and we will restrict ourselves to this first step throughout this paper. The second step involves solving the equation for the nuclear motion. Having completed both

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On the use of explicitly correlated functions in variational computations for small molecules

Abstract: The explicitly correlated wave functions used in variational molecular calculations are reviewed. Different types of such functions are considered. The state of art and future perspectives are briefly discussed. 0

Cited by 27 publications

References 91 publications

Explicitly correlated Gaussian functions in variational calculations: The ground state of the beryllium atom

Explicitly correlated Gaussian functions in variational calculations: The ground state of the beryllium atom

The nuclear magnetic shielding and spin-rotation constants of the hydrogen molecule

The Role of Efficient Programming in Theoretical Chemistry and Physics Problems

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