Relativistic Correction from the Four-Body Nonadiabatic Exponential Wave Function.

We present a method for calculating the relativistic correction in hydrogen molecules that significantly exceeds the accuracy of all the previous literature results. This method utilizes the explicitly correlated nonadiabatic exponential wave function, and thus treats electrons and nuclei equivalently. The proposed method can be applied to any rovibrational state, including highly excited ones.

Hyperfine Structure of the First Rotational Level in H_{2}, D_{2} and HD Molecules and the Deuteron Quadrupole Moment.

We perform the four-body calculation of the hyperfine structure in the first rotational state J=1 of the H_{2}, D_{2}, and HD molecules and determine the accurate value for the deuteron electric quadrupole moment Q_{d}=0.285 699(15)(18)  fm^{2} in significant disagreement with former spectroscopic determinations. Our results for the hyperfine parameters agree very well with the currently most accurate molecular-beam magnetic resonance measurement performed several decades ago by N.

Nonrelativistic energy levels of D.

Nonrelativistic energies of the deuterium molecule, accurate to 10-7-10-8 cm-1 for all levels located up to 8000 cm-1 above the ground state, are presented. The employed nonadiabatic James-Coolidge wave functions with angular factors enable the high accuracy to be reached regardless of vibrational or rotational quantum number. The derivative of the energy with respect to the deuteron-to-electron mass ratio is supplied for each level, which makes the results independent of the future changes in this physical parameter and will enable its determination from sufficiently accurate experimental data.

Nonadiabatic QED Correction to the Dissociation Energy of the Hydrogen Molecule.

The quantum electrodynamic correction to the energy of the hydrogen molecule has been evaluated without expansion in the electron-proton mass ratio. The obtained results significantly improve the accuracy of theoretical predictions reaching the level of 1 MHz for the dissociation energy, in very good agreement with the parallel measurement [Hölsch et al., Phys.

Nonrelativistic energy levels of HD.

Nonadiabatic exponential functions are employed to solve the four-body Schrödinger equation. Nonrelativistic bound energy levels of the HD molecule are calculated to the relative accuracy of 10-10, which is the first step toward highly accurate prediction of dissociation and transition energies. Such energies, in connection with equally accurate experimental data, will enable refinement of the physical constant and aid the search for deviations caused by yet unknown interactions at the atomic scale.

Nonadiabatic Relativistic Correction to the Dissociation Energy of H_{2}, D_{2}, and HD.

The relativistic correction to the dissociation energy of H_{2}, D_{2}, and HD molecules has been accurately calculated without expansion in the small electron-nucleus mass ratio. The obtained results indicate the significance of nonadiabatic effects and resolve the discrepancy of theoretical predictions with recent experimental values for H_{2} and D_{2}. While the theoretical accuracy is now significantly improved and is higher than the experimental one, we observe about 3σ discrepancy for the dissociation energy of HD, which requires further investigation.

Nuclear Spin-Spin Coupling in HD, HT, and DT.

The interaction between nuclear spins in a molecule is exceptionally sensitive to the physics beyond the standard model. However, all present calculations of the nuclear spin-spin coupling constant J are burdened by computational difficulties, which hinders the comparison to experimental results. Here, we present a variational approach and calculate the constant J in the hydrogen molecule with the controlled numerical precision, using the adiabatic approximation.

Nonadiabatic rotational states of the hydrogen molecule.

We present a new computational method for the determination of energy levels in four-particle systems like H, HD, and HeH using explicitly correlated exponential basis functions and analytic integration formulas. In solving the Schrödinger equation, no adiabatic separation of the nuclear and electronic degrees of freedom is introduced. We provide formulas for the coupling between the rotational and electronic angular momenta, which enable calculations of arbitrary rotationally excited energy levels.

Complete α^{6} m Corrections to the Ground State of H_{2}.

We perform the calculation of all relativistic and quantum electrodynamic corrections of the order of α^{6} m to the ground electronic state of a hydrogen molecule and present improved results for the dissociation and the fundamental transition energies. These results open the window for the high-precision spectroscopy of H_{2} and related low-energy tests of fundamental interactions.

Schrödinger equation solved for the hydrogen molecule with unprecedented accuracy.

The hydrogen molecule can be used for determination of physical constants, including the proton charge radius, and for improved tests of the hypothetical long range force between hadrons, which require a sufficiently accurate knowledge of the molecular levels. In this work, we perform the first step toward a significant improvement in theoretical predictions of H2 and solve the nonrelativistic Schrödinger equation to the unprecedented accuracy of 10(-12). We hope that it will inspire a parallel progress in the spectroscopy of the molecular hydrogen.

Leading order nonadiabatic corrections to rovibrational levels of H2, D2, and T2.

An efficient computational approach to nonadiabatic effects in the hydrogen molecule (H2, D2, and T2) is presented. The electronic wave function is expanded in the James-Coolidge basis set, which enables obtaining a very high accuracy of nonadiabatic potentials. A single point convergence of the potentials with growing size of the basis set reveals a relative accuracy ranging from 10(-8) to 10(-13).

Frequency-dependent polarizability of helium including relativistic effects with nuclear recoil terms.

Future metrology standards will be partly based on physical quantities computed from first principles rather than measured. In particular, a new pressure standard can be established if the dynamic polarizability of helium can be determined from theory with an uncertainty smaller than 0.2 ppm.

Accurate adiabatic correction in the hydrogen molecule.

A new formalism for the accurate treatment of adiabatic effects in the hydrogen molecule is presented, in which the electronic wave function is expanded in the James-Coolidge basis functions. Systematic increase in the size of the basis set permits estimation of the accuracy. Numerical results for the adiabatic correction to the Born-Oppenheimer interaction energy reveal a relative precision of 10(-12) at an arbitrary internuclear distance.

Rovibrational levels of helium hydride ion.

Dissociation energy (D(0)) of rovibrational levels of (4)HeH(+) has been predicted theoretically to the accuracy of the order of 0.01 cm(-1). The calculations take into account adiabatic and nonadiabatic corrections as well as relativistic and quantum electrodynamics effects.

Effects of adiabatic, relativistic, and quantum electrodynamics interactions on the pair potential and thermophysical properties of helium.

The adiabatic, relativistic, and quantum electrodynamics (QED) contributions to the pair potential of helium were computed, fitted separately, and applied, together with the nonrelativistic Born-Oppenheimer (BO) potential, in calculations of thermophysical properties of helium and of the properties of the helium dimer. An analysis of the convergence patterns of the calculations with increasing basis set sizes allowed us to estimate the uncertainties of the total interaction energy to be below 50 ppm for interatomic separations R smaller than 4 bohrs and for the distance R = 5.6 bohrs.

Onset of Casimir-Polder retardation in a long-range molecular quantum state.

Two 4He atoms form a diatomic molecule with a significant vibrational wave function amplitude at interatomic separations R>100  Å, where the retardation switches the London R(-6) decay of the potential to the Casimir-Polder R(-7) form. It has been assumed that this effect of retardation on the long-range part of the potential is responsible for the 2 Å (4%) increase of the bond length of 4He2. We show that is, unexpectedly, insensitive to the potential at R>20  Å and its increase is due to quantum electrodynamics effects computed by us from expressions valid at short R--beyond the validity range of Casimir-Polder theory--that seamlessly extend this theory to distances relevant for properties of long molecules.

The absorption spectrum of D2: ultrasensitive cavity ring down spectroscopy of the (2-0) band near 1.7 μm and accurate ab initio line list up to 24,000 cm(-1).

Eleven very weak electric quadrupole transitions Q(2), Q(1), S(0)-S(8) of the first overtone band of D(2) have been measured by very high sensitivity CW-cavity ring down spectroscopy (CRDS) between 5850 and 6720 cm(-1). The noise equivalent absorption of the recordings is on the order of α(min) ≈ 3 × 10(-11) cm(-1). By averaging a high number of spectra, the noise level was lowered to α(min) ≈ 4 × 10(-12) cm(-1) in order to detect the S(8) transition which is among the weakest transitions ever detected in laboratory experiments (line intensity on the order of 1.

The absorption spectrum of H2: CRDS measurements of the (2-0) band, review of the literature data and accurate ab initio line list up to 35000 cm(-1).

Five very weak transitions-O(2), O(3), O(4), O(5) and Q(5)-of the first overtone band of H(2) are measured by very high sensitivity CW-Cavity Ring Down Spectroscopy (CRDS) between 6900 and 7920 cm(-1). The noise equivalent absorption of the recordings is on the order of α(min)≈ 5 × 10(-11) cm(-1) allowing for the detection of the O(5) transition with an intensity of 1.1 × 10(-30) cm per molecule, the smallest intensity value measured so far for an H(2) absorption line.

Quantum Electrodynamics Effects in Rovibrational Spectra of Molecular Hydrogen.

The dissociation energies from all rovibrational levels of H2 and D2 in the ground electronic state are calculated with high accuracy by including relativistic and quantum electrodynamics (QED) effects in the nonadiabatic treatment of the nuclear motion. For D2, the obtained energies have theoretical uncertainties of 0.001 cm(-1).

Collision-induced dipole polarizability of helium dimer from explicitly correlated calculations.

Large expansions in basis sets of explicitly correlated Gaussian functions and the variation-perturbation technique were used to calculate the static dipole polarizability of the helium dimer at 16 different internuclear separations from 1.0 to 9.0 bohrs.

Rovibrational levels of HD.

The dissociation energies of all rotation-vibrational states of the molecular HD in the ground electronic state are calculated to a high accuracy by including nonadiabatic, relativistic alpha(2), and quantum electrodynamic alpha(3) effects, with approximate treatment of small higher order alpha(4), and finite nuclear size corrections. The obtained result for the ground molecular state of 36 405.7828(10) cm(-1) is in a small disagreement with the latest most precise experimental value.

Isotope shifts of the three lowest 1S states of the B+ ion calculated with a finite-nuclear-mass approach and with relativistic and quantum electrodynamics corrections.

We present very accurate quantum mechanical calculations of the three lowest S-states [1s(2)2s(2)((1)S(0)), 1s(2)2p(2)((1)S(0)), and 1s(2)2s3s((1)S(0))] of the two stable isotopes of the boron ion, (10)B(+) and (11)B(+). At the nonrelativistic level the calculations have been performed with the Hamiltonian that explicitly includes the finite mass of the nucleus as it was obtained by a rigorous separation of the center-of-mass motion from the laboratory frame Hamiltonian. The spatial part of the nonrelativistic wave function for each state was expanded in terms of 10,000 all-electron explicitly correlated Gaussian functions.

Isotope shift in the electron affinity of lithium.

Very accurate electron affinity (EA) calculations of (6)Li and (7)Li (and (infinity)Li) have been performed using explicitly correlated Gaussian functions and a variational approach that explicitly includes the nuclear motion in the calculations (i.e., the approach that does not assume the Born-Oppenheimer approximation).

Theoretical Determination of the Dissociation Energy of Molecular Hydrogen.

The dissociation energy of molecular hydrogen is determined theoretically with a careful estimation of error bars by including nonadiabatic, relativistic, and quantum electrodynamics (QED) corrections. The relativistic and QED corrections were obtained at the adiabatic level of theory by including all contributions of the order α(2) and α(3) as well as the major (one-loop) α(4) term, where α is the fine-structure constant. The computed α(0), α(2), α(3), and α(4) components of the dissociation energy of the H2 isotopomer are 36 118.

Rovibrational energy levels of H3(+) with energies above the barrier to linearity.

The H(3)(+) potential energy surface is sampled at 5900 geometries with the emphasis on the nonequilibrium and asymptotic points. Apart from the Born-Oppenheimer energy converged to the accuracy better than 0.02 cm(-1), the adiabatic and the leading relativistic corrections are computed at each geometry.