Nonadiabatic molecular theory and its application. II. Water molecule

Shigeta, Yoshie; Ozaki, Yasushi; Kodama, Kodo; Nagao, Hidemi; Kawabe, Hiroyuki; Nishikawa, Kazuhiro

doi:10.1002/(sici)1097-461x(1998)69:5<629::aid-qua1>3.3.co;2-u

Cited by 17 publications

(23 citation statements)

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“…Lathouwers and coworkers 62–64 have applied the GCM technique to molecular systems and investigated the vibrational levels of hydrogen molecules. Shigeta et al 36 first formulated the GCM in the non‐BO problem, which adopted the total Hamiltonian contaminating the translational and rotational motions. We further propose a hybrid method combining the GCM technique with the TRF‐NOMO model, namely, TRF‐NOMO/GCM 35.…”

Section: Excited‐state Methods For Non‐bo Problemmentioning

confidence: 99%

“…Such an orbital approach, termed the nuclear orbital plus molecular orbital (NOMO) method, simultaneously determines nuclear and electronic wave functions without BO approximation by using the NOs and MOs. Recently, orbital approaches for the non‐BO problem has been studied in other groups as well 36–55. In principle, the NOMO treatment is capable of giving the exact solution for the non‐BO problem, as discussed in Section 2.…”

Section: Introductionmentioning

confidence: 99%

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Nuclear orbital plus molecular orbital theory: Simultaneous determination of nuclear and electronic wave functions without Born–Oppenheimer approximation

Nakai

2007

Int J of Quantum Chemistry

100

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ABSTRACT:We review a recent development in a rigorous non-Born-Oppenheimer method, i.e., nuclear orbital plus molecular orbital (NOMO) method, which determines the nuclear and electronic wave functions simultaneously. The NOMO theory is an exact theory for the non-BO problem in principle; for example, full-configuration interaction formulation for a complete configuration space. Hartree-Fock (HF) equations for NOs and MOs are derived for practical calculations. The usage of Gaussian basis functions for NOs is discussed. We formulate the elimination of translational and rotational contaminations in the NOMO method. Further, many-body effect such as nucleus-nucleus (n-n), nucleuselectron (n-e), and electron-electron (e-e) correlations are investigated by applying the second-order Møller-Plesset perturbation theory to the NOMO method. The excited-state theories such as configuration interaction and generator coordinate methods are examined to describe not only electronic but also vibrational excited states.

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Section: Excited‐state Methods For Non‐bo Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nuclear orbital plus molecular orbital theory: Simultaneous determination of nuclear and electronic wave functions without Born–Oppenheimer approximation

Nakai

2007

Int J of Quantum Chemistry

100

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“…Theoretically, to obtain the protonic structure of molecules (methane, ammonia, water, and hydrogen fluoride), Thomas 17–20 proposed the methodology of molecular quantum mechanics in 1969–1970 that the protons as well as electrons are described by Slater determinants of one‐particle Slater functions. After that, several approaches using non‐BO schemes have been applied to the treatment of nuclear quantum effects in molecular systems 21–116. Adamowicz and coworkers 25–54 proposed the high accuracy non‐BO calculations using nonadiabatic Hamiltonian and the center‐of‐mass transformation with explicitly correlated Gaussian (ECG) functions.…”

Section: Introductionmentioning

confidence: 99%

Review of multicomponent molecular orbital method for direct treatment of nuclear quantum effect

Ishimoto

Tachikawa

Nagashima

2009

Int J of Quantum Chemistry

101

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ABSTRACT:We present the methodology and applications of multicomponent molecular orbital (MC_MO) method, which can take into account of the quantum effect of light particles, such as proton and deuteron, directly. We summarize the equations of the MC_MO method at the Hartree-Fock (HF) level and beyond the HF. The methodology of the MC_MO with fragment molecular orbital (FMO) method for large molecular systems is also described. We discuss the development of nuclear basis function based on the GTF, which is used in MC_MO and FMO-MC_MO calculations. We present the applications of MC_MO and FMO-MC_MO method for the analysis of geometrical isotope effect and kinetic isotope effect induced by H/D isotope effect. Key words: multicomponent molecular orbital (MC_MO) method; FMO-MC_MO method; nuclear quantum effect; H/D isotope effect

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“…For the former theory, we generalized Thomas' protonic structure concept 92 to polyatomic systems by means of a linear combination of both electronic and nuclear one-particle orbitals. At first we adopted a generator coordinate method to estimate electronic and vibronic excited states, 22 and then reformulated by using non-BornOppenheimer density functional theory (NBO-DFT) 23 and Green's function theory. 24 Nakai and Tachikawa also derived the same methodology at almost the same time 34 and developed post self-consistent field methods.…”

Section: Theoretical Development Of Quantum Effects Of Nucleimentioning

confidence: 99%

Molecular Theory Including Quantum Effects and Thermal Fluctuations

Shigeta

2009

Bulletin of the Chemical Society of Japan

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Recent progress in our theoretical developments and applications where thermal fluctuations and quantum effects are important are reviewed. We first show that motions of a confined atom coupled with a fullerene cage cause large thermal fluctuation of the effective charge on the confined atom and that the fluctuation is sensitive to applied temperature and the number of confined species. Second, two different approaches to treat nuclear quantum effects are discussed. One is nonBornOppenheimer (NBO) molecular theory, which is one of an extension of molecular orbital theory for electrons to nuclear motions. This method is suitable to describe static and stationary nuclear (vibrational) states so we apply this method to obtain vibrationally coupled electron density of a protonatable amino acid. We compare the obtained electron density through NBO treatment with conventional calculations. The other approach is referred as to quantum cumulant dynamics (QCD), which is a generalization of quantized Hamiltonian dynamics initially proposed by Prezhdo. This method is applied to vibrational analyses. The ordinary normal mode analysis (NMA) is extended to include quantum degrees of freedom based on QCD formalism, which gives a better description of the vibrational state, where ordinary NMA gives incorrect results. Vibrational frequencies of small molecules by the QCD simulation are compared with those by classical molecular dynamics (MD). It is found that QCD is superior to classical MD in that the results obtained by QCD are in good agreement with those by full quantum treatment. Finally the theoretical background of a real-space gridbased time-dependent density functional theory (RSTDDFT) is explained. This method is applied to solve a NBO problem by using an imaginary time propagator and electron dynamics driven by an off-resonant circularly polarized laser plus in addition to using a real time propagator. For the latter case, we investigate atom-centered dipole moment and induced current and detect the electronic fluctuation in a SiH 4 molecule after irradiation.

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Nonadiabatic molecular theory and its application. II. Water molecule

Cited by 17 publications

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Nuclear orbital plus molecular orbital theory: Simultaneous determination of nuclear and electronic wave functions without Born–Oppenheimer approximation

Nuclear orbital plus molecular orbital theory: Simultaneous determination of nuclear and electronic wave functions without Born–Oppenheimer approximation

Review of multicomponent molecular orbital method for direct treatment of nuclear quantum effect

Molecular Theory Including Quantum Effects and Thermal Fluctuations

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