Molecular Bonding in an Orbital-Free-Related Density Functional Theory

Abstract

A density functional theory based on polymer self-consistent field theory is applied to systems of two atoms in order to show that this approach is capable of predicted molecular bonding. Periodic table elements from hydrogen up to neon are examined and homonuclear diatomic molecules are found to form for H 2 , N 2 , O 2 , and F 2 , in agreement with known results. The heteronuclear molecules CO and HF, which are known to exist under ambient conditions, are also found to be stable. Bond lengths for most of these molecules agree with experimental results to within less than 8%, with the exception of O 2 and F 2 which deviate more significantly. The bonding energy for H 2 is given and is within 16% of the known value, but fundamental vibrational frequencies do not agree well with experiment. The main approximations of the theory are very simple and include a Fermi−Amaldi correction to the electron−electron interaction to account for self-interactions and a basic expression for the Pauli potential to account for the exclusion principle. The self-consistent equations are solved in terms of basis functions that encode the cylindrical symmetry of diatomic molecules. Since orbitals are not used, the approach is related to orbital-free density functional theory.

An interpretation of quantum foundations based on density functional theory and polymer self-consistent field theory

“…Instead, a classical excluded volume is postulated between threads, or allowing for spin, between pairs of threads. This has been shown to reproduce correct shell structure in atoms [12] and bonding in molecules [29]. These and other predictions follow from performing classical statistical mechanics on this Gaussian thread model of quantum particles following the methods of polymer SCFT.…”

“…The method can also be used to find the geometry of molecules by moving the ion centres, each time solving the electron density self-consistently, until the electronic free energy is minimized by the positions of the ions. In reference [29], the bond lengths and bond energies of a number of diatomic molecules were found using a basis set of Fourier series and cylindrical Bessel functions for the z and ρ directions, respectively. Since the Heisenberg uncertainty principle is built-in to the SCFT approach, being manifested in the extended thread nature of the particles, only the basis function set needs to be changed to consider different system symmetries.…”

A Holographic Principle for Non-Relativistic Quantum Mechanics

“…Just as q(r, r, β) is the mathematical expression of thermal-world-line statistics in the static case, (21) demonstrates that the classical thread picture of quantum particles in 5D is consistent with quantum dynamics, even if on a practical level, one uses the equations of TDDFT, including (20), as a black-box to perform calculations in terms of complex eigenfunctions.…”

“…SCFT mathematics predict, using a 5D classical framework without wave functions, the stability and shell structure of atoms [11,16,18], spontaneous spherical symmetry breaking in atoms [19], molecular bonding [20], and even the spontaneous emergence of classical electromagnetism [12]. In this paper, many of these features of SCFT, as presented at the 15th Biennial Quantum Structure Conference, are reviewed and other topics which arose in the questions and discussions following the presentation are explained, such as quantum statistics, the uncertainty principle, quantum kinetic energy, tunnelling, the double slit experiment, geometric phase including the Aharonov-Bohm effect, entanglement, exchange, and the Pauli exclusion principle.…”

“…In this paper, many of these features of SCFT, as presented at the 15th Biennial Quantum Structure Conference, are reviewed and other topics which arose in the questions and discussions following the presentation are explained, such as quantum statistics, the uncertainty principle, quantum kinetic energy, tunnelling, the double slit experiment, geometric phase including the Aharonov-Bohm effect, entanglement, exchange, and the Pauli exclusion principle. First principles derivations, numerical methods and more detailed discussions of SCFT applied to quantum systems can be found in references [11,12,16,[18][19][20].…”