Heitler-London Method Research Articles

A commentary on Weisberg’s critique of the ‘structural conception’ of chemical bonding

Robin Hendry has presented an account of two equally valid ways of understanding the nature of chemical bonding, consisting of what the terms the structural and the energetic views respectively. In response, Weisberg has issued a “challenge to the structural view”, thus implying that the energetic view is the more correct of the two conceptions. In doing so Weisberg identifies the delocalization of electrons as the one robust feature that underlies the increasingly accurate quantum mechanical calculations starting with the Heitler-London method and moving on to such approaches as the valence bond and molecular orbital theories of chemical bonding. The present article provides a critical evaluation of Weisberg’s article and concludes that he fails to characterize the nature of chemical bonding in several respects. I claim that Hendry’s structural and energetic views remain as equally viable ways of understanding chemical bonding. Whereas the structural view is more appropriate for chemists, the energetic view is preferable to physicists. Neither view is more correct unless one subscribes to the naively reductionist view of considering that the more physical energetic view is the more correct one.

Study of the structures of four-quark states in terms of the Born-Oppenheimer approximation**Supported by National Natural Science Foundation of China (11375128)

In this work, we use the Born-Oppenheimer approximation, where the potential between atoms can be approximated as a function of distance between the two nuclei, to study the four-quark bound states. By this approximation, Heitler and London calculated the spectrum of the hydrogen molecule, which includes two protons (heavy) and two electrons (light). Generally, the observed exotic mesons Zb(10610), Zb(10650), Zc(3900) and Zc(4020) (Zc(4025)) may be molecular states made of two physical mesons and/or diquark-anti-diquark structures. Analogous to the Heitler-London method for calculating the mass of the hydrogen molecule, we investigate whether there exist energy minima for these two structures. Contrary to the hydrogen molecule case where only the spin-triplet possesses an energy minimum, there exist minima for both of these states. This implies that both molecule and tetraquark states can be stable objects. Since they have the same quantum numbers, however, the two states may mix to result in the physical states. A consequence would be that partner exotic states co-existing with Zb (10610), Zb (10650), Zc (3900) and Zc (4020) (Zc (4025)) are predicted and should be experimentally observed.

Nonorthogonal orbitals; the Hartree–Fock–Heitler–London method and preliminary applications

AbstractSince the early days of quantum chemical computations, the determinantal wave function can be constructed either with orthogonal or nonorthogonal one electron functions (the orbitals). The two classical quantum mechanical methods, the Hartree–Fock (HF), and the Heitler–London (HL) are examples of the use of orthogonal, and nonorthogonal orbitals, respectively. Both models are approximations yielding approximately half of the experimental binding energy, due to the correlation error. Very extended expansions (with many thousand determinants) recover the error. The two methods have been recently merged into the Hartree–Fock–Heitler–London method (HF–HL), which systematically ensures correct molecular dissociation and a binding energy generally more correct than that obtained with the two parent models. Relatively short expansions of HL configurations yield correct binding energies, at the expense, however, of a high computational time in the optimization of the orbital expansion coefficients. In the HF–HL model, the inner shell electronic correlation is computed with a Coulomb hole functional. We compare computations at the HF, HL, and HF–HL levels, and for the latter, we consider relatively short expansions leading to reasonable binding energies. The computations compare the ground‐state potential energies of the hydrides and homopolar diatomic molecules of the first and second period of the atomic table, a few excited states, and small polyatomic molecules like H2O, C2H2, and HCN. © 2012 Wiley Periodicals, Inc.

Size dependence of biexciton binding energy in single InAs/GaAs quantum dots

This paper studies the size dependence of biexciton binding energy in single quantum dots (QDs) by using atomic force microscopy and micro-photoluminescence measurements. It finds that the biexciton binding energies in the QDs show “binding" and “antibinding" properties which correspond to the large and small sizes of QDs, respectively. The experimental results can be well interpreted by the biexciton potential curve, calculated from the exciton molecular model and the Heitler–London method.

Size effects in the exchange coupling between two electrons confined in quantum wire quantum dots

We theoretically investigate the properties of a two-electron system confined in the three-dimensional potential of coupled quantum dots formed in a quantum wire. For this purpose, we implement a variational Heitler-London method that minimizes the system energies with respect to variational parameters in electron trial wave functions. We find that tunnel and exchange couplings rapidly decay with increasing interdot distance and interdot barrier height. In the quasi-one-dimensional limit achieved by reducing the wire diameter, we find that the overlap between the dots decreases, which results in a drop in the exchange coupling. We also discuss the validity of our variational Heitler-London method with respect to the model potential parameters; we find good agreement between our results and available experimental data.

On dipole moments of overlapping atoms. Application to H in 1 s, 2 s, and 2po states

The dipole moments of two overlapping H atoms in the dissimilar states 1 s, 2 s and 2p$_{o}$ were calculated for both the triplet (destructive overlap) and the singlet (constructive overlap) states at large separations. The results are based on the Heitler-London method, using elliptical coordinates with the nucleus of the larger, more diffused orbital, located at a on the Z-axis of the coordinate system, and the nucleus of the smaller, less diffused orbital, located at b on the Z-axis. The origin of the coordinate system is midway between a and b. We find it instructive to identify three types of moments - a moment associated with the orbital on a, a moment associated with the orbital on b, and the overall moment, which is the sum of these two. It is shown that in the region of small overlap the calculated values of the dipoles on a and on b point towards each other in the triplet state, and away from each other in the singlet state. In every case, the total or net dipole moment points from the more diffused orbital towards the more compact orbital. The absolute value of the more diffused orbital is always found to be greater than of the more rigid orbital.

Effect of an inhomogeneous external magnetic field on a quantum-dot quantum computer

We calculate the effect of an inhomogeneous magnetic field, which is invariably present in an experimental environment, on the exchange energy of a double quantum dot artificial molecule, projected to be used as a 2-qubit quantum gate in the proposed quantum dot quantum computer. We use two different theoretical methods to calculate the Hilbert space structure in the presence of the inhomogeneous field: the Heitler-London method which is carried out analytically and the molecular orbital method which is done computationally. Within these approximations we show that the exchange energy J changes slowly when the coupled dots are subject to a magnetic field with a wide range of inhomogeneity, suggesting swap operations can be performed in such an environment as long as quantum error correction is applied to account for the Zeeman term. We also point out the quantum interference nature of this slow variation in exchange.

Excitons, biexcitons, and the band gap in poly(p-phenylene vinylene).

The excited states of poly(p-phenylene vinylene) (PPV) are studied in the Su-Schrieffer-Heeger model appended by a long-range Coulomb interaction. We have calculated the energy levels of singlet and triplet excitons with odd and even parity, the biexciton state, and the onset of the continuum band in PPV; these results can comprehensively interpret relevant experimental data. More significantly, we have constructed the wave function of the biexciton by using the Heitler-London method and calculated the binding energy and radius of the biexciton in conjugated polymers.

Theoretical calculation for the high pressure properties of alkali fluorides

Abstract The overlap repulsive potentials of ion pairs (Li +−F−, Na+−F− and K+−F−) are calculated by means of generalized Heitler-London method and the numerical results are fitted in the Born-Mayer form, i.e. Dexp (—αR), Then the parameter D for each pair potential is modified to satisfy the crystal equilibrium condition at the experimentally known lattice constant. The redetermined repulsive potentials are applied to calculate the cohesive energies, bulk moduli, equations of state and NaC1–to-CsC1 structural phase transition pressures of LiF, NaF and KF crystals. The results obtained are compared with some other theoretical values and the available experimental data, and good agreement is reached.

Quantum properties of a hydrogen-like particle near a hard wall

An exact solution of the Schrödinger equation for a hydrogen-like atom near a hard wall given by us previously [Kovalenko et al., Phys. Status Solidi (B) 155, 549 (1989)] is used for an investigation of the discrete electronic spectrum, the atom dipole moment and oscillator strengths dependent on the distance from the wall. A hydrogen-like molecular near a hard wall is considered in the framework of the Heitler—London method.

The hydrogen molecule for a two‐dimensional system

The two-dimensional (2D) energy of the hydrogen molecule is carried out by the Heitler-London method. The 2D integrals (which are more localized compared to 3D ones) are performed in the light of the 3D Slater integrals. A discussion of such 2D systems is briefly outlined for doped semiconductors.

Derivation of model Hamiltonians: Exchange Hamiltonian for H2.

The derivation of model Hamiltonians such as crystal-field and spin Hamiltonians requires the decoupling of electrons, which may be done by defining an appropriate equivalent Hamiltonian ${H}_{\mathrm{eq}}$. The connection between ${H}_{\mathrm{eq}}$ and the original Hamiltonian, and between the respective eigenfunctions, is explicitly given. The eigenfunctions of ${H}_{\mathrm{eq}}$ are linear combinations of simple products of atomic spin orbitals, the latter being chosen in such a way that its antisymmetrization leads to a linearly independent set. The problem is then reformulated in a chosen subspace (effective space) via the effective-Hamiltonian formalism. The model Hamiltonian ${H}_{\mathrm{mod}}$ is then obtained by projecting out the undesired degrees of freedom. If in the two-atom two-electron case one keeps in ${H}_{\mathrm{mod}}$ only first-order terms in the interatomic interaction, one gets the usual Heitler-London approximation. For this reason the formulation has been called the extended Heitler-London method. As an illustration the formalism is applied to the ${\mathrm{H}}_{2}$ molecule, where the usual Heisenberg Hamiltonian is rigorously derived and the values of the energy baricenter and magnetic exchange constant are given, up to the second order of perturbation theory.

Two-electron bond approach to chemisorption

A new approach to chemisorption is presented which considers both neutral and ionic configurations of the adsorbate on the same footing. The two-electron bond between the adsorbate and an atom of the metal surface is characterised by the Heitler-London method, the metal band structure being described by the cluster-Bethe lattice method. The only parameter of this theory is the hopping integral of the Anderson-Newns Hamiltonian. Quantities such as charge populations, one electron levels, and excitation energies which can be immediately compared with the spectroscopic data (ELS, UPS, ESD, etc.) can be easily deduced. An application is given to the H/W(100) system.

Heisenberg spin Hamiltonian through a new Heitler-London approach: Test on the half-filled linear Hubbard model

The Heisenberg spin Hamiltonian constructed from a new Heitler-London method is tested on the half-filled linear Hubbard model. It is found that the Heisenberg Hamiltonian of the new Heitler-London method works well in a much wider parameter range than that of the usual perturbation method does.

Potential-energy function of two hydrogen atoms around a platinum atom which protrudes from a metallic-platinum surface

A model calculation of the potential-energy function of two H atoms around a Pt atom that protrudes from a smooth metallic-Pt surface has been performed using the Heitler-London method. It is found that the potential energy is minimum along two contours; along one contour, the two H atoms combine as a molecule, while along the second contour, they are separated not only geometrically but also electronically when the Pt-H separation is larger than about 2.4a0.

Potential energy curves and excitation transfer cross sections of excited hydrogen atoms

The complete set of potential energy curves arising from the interaction between H(1s) and H(3s, 3p, 3d) has been computed by means of the Heitler-London method. These values have been used for calculating the excitation transfer cross section of the process H(1s)+H(3s, 3p, 3d)=H(3s, 3p, 3d)+H(1s) as a function of the relative energy. The results have been compared with the corresponding values for the principle quantum number 2.

On the complete set of functions in the Heitler–London method for two‐electron problem

AbstractIt is shown that under certain restrictions the system of determinants φi(x1)φk(x2) − φk(x1)ψi(x2) constructed from two different sets of orbitals ψk and φk will be the complete set of functions for antisymmetrical two‐electron wave functions if the condition i < k is imposed.

Migration Energy of an Interstitial He Atom in LiH

The method of lattice statics is used to study the distortion of the LiH crystal with an interstitial He atom in the body-centered or face-centered position. In these calculations, one needs to know the defect-host-ion interaction potentials and the dynamical matrix of the undistorted host crystal. The Heitler-London method is used to estimate the defect-host-ion interaction potentials. The dynamical matrix of the perfect crystal is calculated on the basis of the deformation dipole model. The formation energies are computed for the two defect positions and their difference, 0.650 eV, gives the migration energy of an interstitial He atom in LiH. The calculated migration energy is discussed in light of the high-temperature experimental result for the activation energy of diffusion of He gas in LiH crystal (1.22 eV).

Application of the Pseudopotential Method to Atomic Scattering

The empirical pseudopotential method is discussed and applied to a calculation of the spin-exchange cross section in collisions of Na and Cs atoms. The difference between potential energy curves for the lowest singlet and triplet states of the Na-Cs system is calculated by the Heitler-London method, using a Hamiltonian in which the effects of tightly bound electrons are replaced by a pseudopotential. Wave functions for the free atoms are found by numerical integration using the pseudopotential, and agree well with the exact valence-electron functions at large distances. The scattering phase shifts are calculated in the WKB approximation, and the cross section computed from them is averaged over a Boltzmann distribution of relative velocities. At a temperature of 500\ifmmode^\circ\else\textdegree\fi{}K, the averaged reduced spin-exchange cross section is 1.5 \ifmmode\times\else\texttimes\fi{} 1.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$.

Collisional Transfer of Triplet Excitations between Helium Atoms

The cross sections for 2 3 S and 2 3 P excitation transfer processes between He atoms are calculated by the perturbed stationary state method. The potential energy curves for He(1 1 S)+He * (2 3 P) and He(1 1 S)+He * (2 3 S) systems are obtained by the Heitler-London method taking the configuration interaction between them into account. The calculation involves the transfer, the diffusion and the total elastic cross sections. The results show that the transfer cross section for 2 3 P is 15∼23π a 0 2 at thermal energy and larger than that for 2 3 S. The transfer cross section for 2 3 S dose not so much differ from the calculation using rigorous potentials by Kolker and Michels [J. chem. Phys. 50 (1969) 1762].