Energy and density analyses of the H2 molecule from the united atom to dissociation: The ∑1g+ states

Solving the Schrödinger equation of hydrogen molecule with the free complement-local Schrödinger equation method: Potential energy curves of the ground and singly excited singlet and triplet states, Σ, Π, Δ, and Φ

The free-complement (FC) theory for solving the Schrödinger equation (SE) was applied to calculate the potential energy curves of the ground and excited states of the hydrogen molecule (H₂) with the ¹Σ_g ⁺, ¹Σ_u ⁺, ³Σ_g ⁺, ³Σ_u ⁺, ¹Π_g, ¹Π_u, ³Π_g, ³Π_u, ¹Δ_g, ¹Δ_u, ³Δ_g, ³Δ_u, ¹Φ_g, ¹Φ_u, ³Φ_g, and ³Φ_u symmetries (in total, 54 states). The initial functions of the FC theory were formulated based on the atomic states of the hydrogen atom and its positive and negative ions at the dissociation limits. The local Schrödinger equation (LSE) method, which is a simple sampling-type integral-free methodology, was employed instead of the ordinary variational method and highly accurate results were obtained stably and smoothly along the potential energy curves. Thus, with the FC-LSE method, we succeeded to perform the comprehensive studies of the H₂ molecule from the ground to excited states belonging up to higher angular momentum symmetries and from equilibriums to dissociation limits with almost satisfying spectroscopic accuracy, i.e., 10^-6 hartree order around 1 cm^-1, as absolute solutions of the SE by moderately small calculations.

Solving the Schrödinger equation of hydrogen molecules with the free-complement variational theory: essentially exact potential curves and vibrational levels of the ground and excited states of the Σ symmetry

The Schrödinger equation of hydrogen molecules was solved essentially exactly and systematically for calculating the potential energy curves of the electronic ground and excited states of the ¹Σ_g, ¹Σ_u, ³Σ_g, and ³Σ_u symmetries. The basic theory is the variational free complement theory, which is an exact general theory for solving the Schrödinger equation of atoms and molecules. The results are essentially exact with the absolute energies being correct beyond μ-hartree digits. Furthermore, all of the present wave functions satisfy correct orthogonalities and Hamiltonian-orthogonalities to each other at every nuclear distance along the potential curve, which makes systematic analyses and discussions possible among all the calculated electronic states. It is noteworthy that these conditions were not satisfied in many of the accurate calculations of H₂ reported so far. Based on the present essentially exact potential curves, we calculated and analyzed the vibrational energy levels associated with all the electronic states. Among them, the excited states having double-well potentials showed some interesting features of the vibrational states. These results are worthy of future investigations in astronomical studies.

Unexpectedly high pressure for molecular dissociation in liquid hydrogen by electronic simulation

The study of the high pressure phase diagram of hydrogen has continued with renewed effort for about one century as it remains a fundamental challenge for experimental and theoretical techniques. Here we employ an efficient molecular dynamics based on the quantum Monte Carlo method, which can describe accurately the electronic correlation and treat a large number of hydrogen atoms, allowing a realistic and reliable prediction of thermodynamic properties. We find that the molecular liquid phase is unexpectedly stable, and the transition towards a fully atomic liquid phase occurs at much higher pressure than previously believed. The old standing problem of low-temperature atomization is, therefore, still far from experimental reach.

Electron pair density in the lowest 1Σ(u)(+) and 1Σ(g)(+) states of H2

We demonstrate and advocate the use of observable quantities derived from the two-electron reduced density matrix - pair densities, conditional densities, and exchange-correlation holes--as signatures of the type of electron correlation in a chemical bond. The prototype cases of the lowest (1)Σ(u)(+) and (1)Σ(g)(+) states of H(2), which exhibit large variation in types of bonding, ranging from strongly ionic to covalent, are discussed. Both the excited (1)Σ(g)(+) and (1)Σ(u)(+) states have been interpreted as essentially consisting of (natural) orbital configurations with an inner electron in a contracted 1sσ(g) orbital and an outer electron in a diffuse (united atom type, Rydberg) orbital. We show that nevertheless totally different correlation behavior is encountered in various states when comparing them at a common internuclear distance. Also when following one state along the internuclear distance coordinate, strong variation in correlation behavior is observed, as expected. Switches between ionic to covalent character of a state occur till very large distances (40 bohrs for states approaching the 1s3[script-l] asymptotic limit, and 282 bohrs for states approaching the 1s4[script-l] limit).

Energy and density analysis of the H2 molecule from the united atom to dissociation: the 3Sigma(g)+ and 3Sigma(u)+ states

The first 14 (3)Sigma(g)(+) and the first 15 (3)Sigma(u)(+) states of the H(2) molecule are computed with full configuration interaction both from Hartree-Fock molecular orbitals and Heitler-London atomic orbitals within the Born-Oppenheimer approximation, following recent studies for the (1)Sigma(g)(+) and (1)Sigma(u)(+) manifolds [Corongiu and Clementi, J. Chem. Phys. 131, 034301 (2009) and J. Phys. Chem. (in press)]. The basis sets utilized are extended and optimized Slater-type functions and spherical Gaussian functions. The states considered correspond to the configurations (1s(1)nl(1)) with n from 1 to 5; the internuclear separations sample the distances from 0.01 to 10,000 bohrs. For the first three (3)Sigma(g)(+) and (3)Sigma(u)(+) states and for the fourth and fifth (3)Sigma(g)(+) states, our computed energies at the equilibrium internuclear separation, when compared to the accurate values by Staszewska and Wolniewicz and by Kołos and Rychlewski, show deviations of about 0.006 kcal/mol, a test on the quality of our computations. Motivation for this work comes not only from obtaining potential energy curves for the high excited states of H(2) but also from characterizing the electronic density evolution from the united atom to dissociation to provide a detailed analysis of the energy contributions from selected basis subsets and to quantitatively decompose the state energies into covalent and ionic components. Furthermore, we discuss the origin of the seemingly irregular patterns in potential energy curves in the two manifolds, between 4 and 6-9 bohrs--there are two systems of states: the first, from the united atom to about 4 bohrs, is represented by functions with principal quantum number higher than the one needed at dissociation; this system interacts at around 4 bohrs with the second system, which is represented by functions with principal quantum number corresponding to one of the dissociation products.