One can produce two "isotopes" of the H atom utilizing positive or negative muons, "muonium (0.114 amu) and "muonic helium (4.11 amu)." These isotopes can be used to probe large isotope effects with the mass ratio range exceeding the values of H/D/T isotopes. Due to the extremely small mass of Mu, chemical reactions where a hydrogen atom is replaced by Mu frequently show large quantum mass effects including zero-point energy and tunneling. In addition, there are anomalous examples, by Mu-substitution, where the reaction products are changed and the transition state is energetically stabilized.

We have been developing the first principles calculation methods for the quantum states of small mass atom motion in solid materials and on their surfaces. Our main target atoms are hydrogen isotopes, protium, deuterium, tritium and muonium. We introduce our current method and its some application results. The simulation results show quantitatively good agreement with experimental results. This type of simulation method is not only of academic interest but useful and imperative for developing future materials for hydrogen technology.

Nuclear quantum effect in molecular hydrogens plays an important role to describe the ground state of hydrogen clusters. As an example, we first show ground state properties of (H₂)₁₃; the standard harmonic approximation fails to describe the ground state properties of the cluster, and the wavefunction is found to be delocalized in configuration space covering various local minima of potential energy. We also show chemical potential μ_N as a function of the cluster size for N ≤ 20. We find a minimum of μ_N at N=13 in the size dependence, showing the magic number stability.

A new Colle-Salvetti type electron-nucleus correlation functional for multicomponent density functional theory is proposed. The new functional is derived from an electron-nucleus correlation wavefunction using only simple and reasonable physical corrections with only one fitted parameter. By calculating 18 small hydrogen-containing molecules, this correlation functional is found to quantitatively evaluate these electron-proton correlation energies. The strategy taken in this development is applicable not only to electron-proton correlations but also to electron-other nucleus correlations and even to correlations between electron and other particles like electron-muon and electron-positron correlations.

The nuclear orbital plus molecular orbital (NOMO) method is a quantum chemical theory introducing the concept of orbital into nuclei. The nuclear orbital energy, obtained as a solution of the Hartree-Fock equation for the NOMO method, has not been noticed in comparison with total energy and nuclear orbital itself. In this paper, physical meaning and application of nuclear orbital energy for the NOMO method are discussed. In particular, proton binding energy calculations, based on the recently developed proton propagator method, are mentioned, including examples of calculations.

We recently proposed a real-time simulation method of nuclear and electron wave packet molecular dynamics (NEWPMD) based on wave functions of hydrogen molecules composed of nuclear and electron WPs. Non-empirical intra- and intermolecular interactions of non-spherical hydrogen molecules were explicitly derived and a long-range dispersion force between hydrogen molecules was successfully derived. Nuclear quantum effects (NQEs) such as nuclear delocalization and zero-point energy were non-perturbatively taken into account. The developed NEWPMD method can be applied to various condensed hydrogen systems from a gas-phase to a high-pressure solid phase at feasible computational cost, providing intuitive understandings of real-time dynamics of each hydrogen molecule including H-H bond vibration, molecular orientations and librational motions. We will report the demonstrations not only in liquid hydrogens but also in solid and supercooled hydrogens which exhibited strong NQEs and thus anomalous static and dynamic properties.

Cooperative phenomena between a proton (or hydrogen atom) and an electron play an important role in biological and chemical systems. In crystalline/solid materials, however, such phenomena have scarcely been seen before. Under this circumstance, the authors' continuous synthetic effort has led to the discovery of an interplay between hydrogen-bond dynamics and π-electrons in an organic conductor crystal, providing unprecedented dynamic phenomena, physical properties, and functionality. In this article, this new "quantum-hydrogen science" in π-electron materials is introduced from the viewpoints of the materials synthesis and the hydrogen/deuterium isotope effect.

Quantum effect is manifest for hydrogen atoms on surfaces as well as for those in solution and solids. The excited states of a hydrogen atom directly adsorbed on metal surfaces are beyond the diffusion barrier, thus being delocalized to the next sites, and even spread over the entire surface in the low-coverage limit. In addition, water and hydroxyl group on the surfaces show significant quantum effect, due to tunneling and zero-point motion of the hydrogen atom. We briefly review some experimental and theoretical studies that revealed the quantum effect of the hydrogen atom on the surfaces.

The structure of carbon nanowalls (CNWs) was investigated by transmission electron microscopy (TEM), which indicated clearly the existence of the bent graphene structure in boundary regions between the crystallites of CNWs. The electronic structure of CNWs was measured by ultraviolet photoelectron spectroscopy (UPS) in comparison with highly oriented pyrolitic graphite (HOPG). The interlayer band of CNWs was observed at the same energy as that in HOPG, while the σ − π hybridized bands were observed at the same binding energy as in carbon nanotubes. Combination of UPS and temperature programmed desorption (TPD) measurements investigated deuterium adsorption which preferably occurred in the boundary regions and enhanced the density of states associated with the electronic states of the boundary regions. The first-principles calculation was employed for the bent coronene molecule as a model of the boundary region between the crystallites of CNWs to elucidate the mechanism of the hydrogen adsorption to CNWs. The hydrogen adsorption energies onto both on-top and hollow sites become greater as the bending angle increases, since the electronic structure of the carbon atom at the adsorption site changes from sp² to sp³ hybridization character, clarified by natural bond orbital analysis.

We here review a scheme for estimating the acid dissociation constant (pK_a) based on quantum-chemical calculations combined with a polarizable continuum model, where a parameter is determined for small reference molecules. This scheme enabled us to derive a semiquantitative pK_a value of specific chemical groups and discuss the influence of the surroundings on the pK_a values. As applications, we have derived the pK_a value of the side chain of an amino acid and almost reproduced the experimental value. By using our computing schemes, we showed the influence of hydrogen bonds on the pK_a values in the case of tripeptides, which decreases the pK_a value by 3.0 units for serine in comparison with those of the corresponding monopeptides. The same procedure is also applicable to estimate the standard hydrogen electrode (SHE) potential in aqueous solution. With our computational scheme, the CCSD (T)/aug-cc-pVDZ method provides the SHE potential of 4.52 V, which is almost the same as the experimental SHE potential. This scheme also reproduces well the redox potentials of several typical reactions within almost 0.1 V. B3LYP also gives excellent redox potentials of the same reactions with almost the same accuracy with our new computational scheme.

Focusing on the OH⁻(H₂O)_2–4 clusters, we have theoretically studied the strongly red shifted ionic hydrogen bond (IHB) OH stretching vibration of water molecules directly bound to the hydroxide. Our calculations show that a systematic blue shift of the IHB OH peak is observed with the increase in the number of water molecules in the first solvation shell. Furthermore, we showed that the vibrational signature of the four coordinated hydroxide for OH⁻(H₂O)₄ will be observed in the 2800–3200 cm⁻¹ range.

We analyzed the rotational constants of CH₃O and CD₃O by using the multi-component molecular orbital method, which takes into account the quantum effect of proton and deuteron directly. We clearly observed the difference in C–H and C-D bond lengths due to the anharmonicity of the potential. The rotational constants of CH₃O and CD₃O based on the optimized structures including H/D geometrical isotope effect showed good agreement with the experimental value. We found that the geometrical changes induced by the H/D isotope effect influence the spectroscopic properties, such as rotational constants.

We elucidated the nuclear quantum effect on the intermolecular hydrogen bond of the acetic acid − phosphorous acid anion cluster system, a model system of periplasmic phosphate binding protein (PPBP) which is reported to have a low barrier hydrogen bond (LBHB), employing a multiscale parallel program platform for highly efficient simulation on high performance computers developed by combining a molecular science program NTChem and path integral molecular dynamics (PIMD) method. We analyzed the model system with one intermolecular hydrogen bond and found that the proton in the hydrogen bond is localized to heavy atoms on both ends as seen in typical hydrogen in the classical simulation, treating the nucleus with classical point charges. On the other hand, the proton delocalized in the center region of the hydrogen bond was found in the quantum simulation taking nuclear fluctuation effect into account. The intermolecular hydrogen bond in the acetic acid − phosphorous acid anion cluster system showed the same tendency with LBHB.