A semi-local kinetic energy density functional (KEDF) was constructed based on machine learning (ML). The present scheme adopts electron densities and their gradients up to third-order as the explanatory variables for ML and the Kohn-Sham (KS) kinetic energy density as the response variable in atoms and molecules. Numerical assessments of the present scheme were performed in atomic and molecular systems, including first- and second-period elements. The results of 37 conventional KEDFs with explicit formulae were also compared with those of the ML KEDF with an implicit formula. The inclusion of the higher order gradients reduces the deviation of the total kinetic energies from the KS calculations in a stepwise manner. Furthermore, our scheme with the third-order gradient resulted in the closest kinetic energies to the KS calculations out of the presented functionals.

A semi-local kinetic energy density functional (KEDF) was constructed based on machine learning (ML). The present scheme adopts electron densities and their gradients up to third-order as the explanatory variables for ML and the Kohn-Sham (KS) kinetic energy density as the response variable in atoms and molecules. Numerical assessments of the present scheme were performed in atomic and molecular systems, including first- and second-period elements. The results of 37 conventional KEDFs with explicit formulae were also compared with those of the ML KEDF with an implicit formula. The inclusion of the higher order gradients reduces the deviation of the total kinetic energies from the KS calculations in a stepwise manner. Furthermore, our scheme with the third-order gradient resulted in the closest kinetic energies to the KS calculations out of the presented functionals.

This article proposes a gauge-origin independent formalism of the nuclear magnetic shielding constant in the two-component relativistic framework based on the unitary transformation. The proposed scheme introduces the gauge factor and the unitary transformation into the atomic orbitals. The two-component relativistic equation is formulated by block-diagonalizing the Dirac Hamiltonian together with gauge factors. This formulation is available for arbitrary relativistic unitary transformations. Then, the infinite-order Douglas-Kroll-Hess (IODKH) transformation is applied to the present formulation. Next, the analytical derivatives of the IODKH Hamiltonian for the evaluation of the nuclear magnetic shielding constant are derived. Results obtained from the numerical assessments demonstrate that the present formulation removes the gauge-origin dependence completely. Furthermore, the formulation with the IODKH transformation gives results that are close to those in four-component and other two-component relativistic schemes.

We have implemented a linear-scaling divide-and-conquer (DC)-based higher-order coupled-cluster (CC) and Moller-Plesset perturbation theories (MPPT) as well as their combinations automatically by means of the tensor contraction engine, which is a computerized symbolic algebra system. The DC-based energy expressions of the standard CC and MPPT methods and the CC methods augmented with a perturbation correction were proposed for up to high excitation orders [e.g., CCSDTQ, MP4, and CCSD(2)(TQ)]. The numerical assessment for hydrogen halide chains, polyene chains, and first coordination sphere (C1) model of photoactive yellow protein has revealed that the DC-based correlation methods provide reliable correlation energies with significantly less computational cost than that of the conventional implementations. (C) 2017 Wiley Periodicals, Inc.

This Letter proposes a density functional treatment based on the two-component relativistic scheme at the infinite-order Douglas-Kroll-Hess (IODKH) level. The exchange-correlation energy and potential are calculated using the electron density based on the picture-change corrected density operator transformed by the IODKH method. Numerical assessments indicated that the picture-change uncorrected density functional terms generate significant errors, on the order of hartree for heavy atoms. The present scheme was found to reproduce the energetics in the four-component treatment with high accuracy. (C) 2017 Elsevier B.V. All rights reserved.

We have derived and implemented a universal formulation of the second-order generalized MollerPlesset perturbation theory (GMP2) for spin-dependent (SD) two-component relativistic many-electron Hamiltonians, such as the infinite-order Douglas-Kroll-Hess Hamiltonian for many-electron systems, which is denoted as IODKH/IODKH. Numerical assessments for He- and Ne-like atoms and 16 diatomic molecules show that the MP2 correlation energies with IODKH/IODKH agree well with those calculated with the four-component Dirac-Coulomb (DC) Hamiltonian, indicating a systematic improvement on the inclusion of relativistic two-electron terms. The present MP2 scheme for IODKH/IODKH is demonstrated to be computationally more efficient than that for DC. (c) 2017 Elsevier B.V. All rights reserved.

An open-shell Hartree-Fock (HF) theory for spin-dependent, two-component relativistic calculations, termed the Kramers-unrestricted HF (KUHF) method, is developed. The present KUHF method, which is formulated as a relativistic counterpart of nonrelativistic UHF, is based on quaternion algebra and partly uses time-reversal symmetry. The fundamental characteristics of KUHF are discussed in this study. From numerical assessments, it was revealed that KUHF gives a corresponding solution to nonrelativistic UHF; furthermore, KUHF properly describes spin-orbit interactions. In addition, KUHF can improve the self-consistent field convergence behavior in spin-dependent calculations, for example, for f-block elements.

This Letter examines the enthalpy of formation for 12 transition metal diatomic molecules and 23 transition metal complexes from the viewpoint of effect of the relativistic effect by using the infinite-order Douglas-Kroll-Hess method with the local unitary transformation and three types of pseudopotentials for several levels of theory. The spin-orbit effect contribution to the enthalpy of formation is more than 10 kcal/mol for third transition metal complexes. Frozen orbital approximation at the outermost orbitals in pseudopotential methods shows a contribution to the enthalpy of formation that is more than two times larger than those of inner core orbitals. (C) 2017 Elsevier B.V. All rights reserved.

Arylboronic esters can be used as versatile reagents in organic synthesis, as represented by Suzuki Miyaura cross-coupling. Here we report a serendipitous finding that simple arylboronic esters are phosphorescent in the solid state at room temperature with a lifetime on the order of several seconds. The phosphorescence properties of arylboronic esters are remarkable in light of the general notion that phosphorescent organic molecules require heavy atoms and/or carbonyl groups for the efficient generation of a triplet excited state. Theoretical calculations on phenylboronic acid pinacol ester indicated that this molecule undergoes an out-of-plane distortion at the (pinacol)B-C-ipso moiety in the T-1 excited state, which is responsible for its phosphorescence. A compound survey with 19 arylboron compounds suggested that the phosphorescence properties might be determined by solid-state molecular packing rather than by the patterns and numbers of boron substituents on the aryl units. The present finding may update the general notion of phosphorescent organic molecules.

This letter proposes a relaxation scheme for core electrons based on the frozen core potential method at the infinite-order Douglas-Kroll-Hess level, called FCP-CR. The core electrons are self-consistently relaxed using frozen molecular valence potentials after the valence SCF calculation is performed. The efficiency of FCP-CR is confirmed by calculations of gold clusters. Furthermore, FCP-CR reproduces the results of the all-electron method for the energies of coinage metal dimers and the core ionization energies and core level shifts of vinyl acetate and three tungsten complexes at the Hartree Fock and/or symmetry-adapted cluster configuration interaction levels. (C) 2016 Elsevier B.V. All rights reserved.

Energy fitting schemes based on informatics techniques using hierarchical basis sets with small cardinal numbers were numerically investigated to estimate correlation energies at the complete basis set limits. Numerical validations confirmed that the conventional two-point extrapolation models can be unified into a simple formula with optimal parameters obtained by the same test sets. The extrapolation model was extended to two-point fitting models by a relaxation of the relationship between the extrapolation coefficients or a change of the fitting formula. Furthermore, n-scheme fitting models were developed by the combinations of results calculated at several theory levels and basis sets to compensate for the deficiencies in the fitting model at one level of theory. Systematic assessments on the Gaussian-3X and Gaussian-2 sets revealed that the fitting models drastically reduced errors with equal or smaller computational effort. (c) 2016 Wiley Periodicals, Inc.

This Letter assesses the self-consistent field (SCF) convergence behavior in the generalized Hartree-Fock (GHF) method. Four acceleration algorithms were implemented for efficient SCF convergence in the GHF method: the damping algorithm, the conventional direct inversion in the iterative subspace (DIIS), the energy-DIIS (EDIIS), and a combination of DIIS and EDIIS. Four different systems with varying complexity were used to investigate the SCF convergence using these algorithms, ranging from atomic systems to metal complexes. The numerical assessments demonstrated the effectiveness of a combination of DIIS and EDIIS for GHF calculations in comparison with the other discussed algorithms. (C) 2016 Elsevier B.V. All rights reserved.

An analytical energy gradient for the spin dependent general Hartree-Fock method based on the infinite-order Douglas-Kroll-Hess (IODKH) method was developed. To treat realistic systems, the local unitary transformation (LUT) scheme was employed both in energy and energy gradient calculations. The present energy gradient method was numerically assessed to investigate the accuracy in several diatomic molecules containing fifth- and sixth-period elements and to examine the efficiency in one-, two,, and three-dimensional silver clusters. To arrive at a practical calculation, we also determined the geometrical-parameters of fac-tris(2-phenylpyridine)iridium and investigated the efficiency. The numerical results confirmed that the present method describes highly accurate relativistic effect with high efficiency. The present method can be a powerful scheme for determining geometries of large molecules, including heavy-element atoms.

地球温暖化の原因であるCO₂の排出量を削減する手段としてCO₂回収貯留（CCS）技術が注目されている。このCCS技術の中でも、広く用いられている化学吸収法は、アミンなど塩基性吸収液へCO₂を吸収させる分離過程と加熱によって高濃度のCO₂を放散させる回収過程からなる。これまでCO₂<br>吸収時に要するエネルギーの削減を目指してアミンの研究・開発が行われている。CO₂吸収効率の良いアミンを探す上で、各アミンについてその化学種濃度の経時変化を予測することは重要である。本研究ではアミン－CO₂反応中の素反応を考慮し、群知能を用いることで実験のローディング依存性から平衡定数を予測する反応シミュレータを開発した。またその平衡定数を量子化学計算による反応自由エネルギーから見積もることで、化学種濃度のローディング依存性の予測も行い、広く1級から3級アミンまで扱えるように拡張した。

これまで、コンピュータを用いて反応物から得られる生成物を予測するシステムが多数開発されてきた。しかし、化学反応の複雑さをコンピュータが表現することは難しく、未だ実験化学者に広く利用されるシステムの開発には至っていない。近年、分子のトポロジカルな情報を中心的な記述子として、機械学習を有機化学反応の予測に応用したシステムが優れた予測能を示した。しかしこの手法は、金属種を含む反応など、分子の立体的構造や電子状態が生成物を左右する反応の予測が困難であると考えられる。そこで本研究では、あらゆる化学種に対する反応予測を目指して、量子化学計算により得られる情報を記述子として機械学習を用いるシステムを開発した。本手法は基本的な有機化学の極性反応およびラジカル反応に対して既存手法と同程度の予測精度を示した。本発表では、本手法の詳細および予測精度の量子化学計算条件に対する依存性について検証した結果を報告する。

We investigate the accuracy of two-component Douglas-Kroll-Hess (DKH) methods in calculations of the nuclear volume term ( lnK(nv)) in the isotope fractionation coefficient. lnK(nv) is a main term in the chemical equilibrium constant for isotope exchange reactions in heavy element. Previous work based on the four-component method reasonably reproduced experimental lnK(nv) values of uranium isotope exchange. In this work, we compared uranium reaction lnK(nv) values obtained from the two-component and four-component methods. We find that both higher-order relativistic interactions and spin-orbit interactions are essential for quantitative description of lnK(nv). The best alternative is the infinite-order Douglas-Kroll-Hess method with infinite-order spin-orbit interactions for the one-electron term and atomic-mean-field spin-same-orbit interaction for the two-electron term (IODKH-IOSO-MFSO). This approach provides almost equivalent results for the four-component method, while being 30 times faster. The IODKH-IOSO-MFSO methodology should pave the way toward computing larger and more general molecules beyond the four-component method limits. (c) 2015 Wiley Periodicals, Inc.

:An efficient algorithm for the rapid evaluation of electron repulsion integrals is proposed. The present method, denoted by accompanying coordinate expansion and transferred recurrence relation (ACE-TRR), is constructed using a transfer relation scheme based on the accompanying coordinate expansion and recurrence relation method. Furthermore, the ACE-TRR algorithm is extended for the general-contraction basis sets. Numerical assessments clarify the efficiency of the ACE-TRR method for the systems including heavy elements, whose orbitals have long contractions and high angular momenta, such as f- and g-orbitals.

完全基底関数極限における高精度な電子相関を含んだ電子相関エネルギーを高効率に算出することは化学的精度（1 kcal/mol以内）での量子化学計算を実現するために重要である。これまで種々の電子相関エネルギーの完全基底関数極限への外挿手法や、幾つかの計算レベル・基底関数でのエネルギーを組み合わせた複合法が提案されてきた。本研究では情報学手法を用いてより効率的に、完全基底関数極限におけるCCSD(T)レベルの電子相関エネルギーを算出する手法を提案する。

An algorithm of the accompanying coordinate expansion and recurrence relation (ACE-RR), which is used for the rapid evaluation of the electron repulsion integral (ERI), has been extended to the general-contraction (GC) scheme. The present algorithm, denoted by GC-ACE-RR, is designed for molecular calculations including heavy elements, whose orbitals consist of many primitive functions with and without higher angular momentum such as d- and f-orbitals. The performance of GC-ACE-RR was assessed for (ss vertical bar ss), (pp vertical bar pp), (dd vertical bar dd), and (ff vertical bar ff)-type ERIs in terms of contraction length and the number of GC orbitals. The present algorithm was found to reduce the central processing unit time compared with the ACE-RR algorithm, especially for higher angular momentum and highly contracted orbitals. Compared with HONDOPLUS and GAMESS program packages, GC-ACE-RR computations for ERIs of three-dimensional gold clusters Au-n (n = 1, 2, . . . , 10, 15, 20, and 25) are more than 10 times faster. (C) 2014 Wiley Periodicals, Inc.

:An algorithm of the accompanying coordinate expansion and recurrence relation (ACE-RR), which is used for the rapid evaluation of the electron repulsion integral (ERI), has been extended to the general-contraction (GC) scheme. The present algorithm, denoted by GC-ACE-RR, is designed for molecular calculations including heavy elements, whose orbitals consist of many primitive functions with and without higher angular momentum such as d- and f-orbitals. The performance of GC-ACE-RR was assessed for (ss|ss)-, (pp|pp)-, (dd|dd)-, and (ff|ff)-type ERIs in terms of contraction length and the number of GC orbitals. The present algorithm was found to reduce the central processing unit time compared with the ACE-RR algorithm, especially for higher angular momentum and highly contracted orbitals. Compared with HONDOPLUS and GAMESS program packages, GC-ACE-RR computations for ERIs of three-dimensional gold clusters Aun (n = 1, 2, …, 10, 15, 20, and 25) are more than 10 times faster.

This Letter proposes an accurate scheme using frozen core orbitals, called the frozen core potential (FCP) method, to theoretically connect model potential calculations to all-electron (AE) ones. The present scheme is based on the Huzinaga-Cantu equation combined with spin-free relativistic Douglas-KrollHess Hamiltonians. The local unitary transformation scheme for efficiently constructing the Hamiltonian produces a seamless extension to the FCP method in a relativistic framework. Numerical applications to coinage diatomic molecules illustrate the high accuracy of this FCP method, as compared to AE calculations. Furthermore, the efficiency of the FCP method is also confirmed by these calculations. (C) 2014 Elsevier B.V. All rights reserved.

:In this study, the analytical energy gradient for the spin-free infinite-order Douglas-Kroll-Hess (IODKH) method at the levels of the Hartree-Fock (HF), density functional theory (DFT), and second-order Møller-Plesset perturbation theory (MP2) is developed. Furthermore, adopting the local unitary transformation (LUT) scheme for the IODKH method improves the efficiency in computation of the analytical energy gradient. Numerical assessments of the present gradient method are performed at the HF, DFT, and MP2 levels for the IODKH with and without the LUT scheme. The accuracies are examined for diatomic molecules such as hydrogen halides, halogen dimers, coinage metal (Cu, Ag, and Au) halides, and coinage metal dimers, and 20 metal complexes, including the fourth-sixth row transition metals. In addition, the efficiencies are investigated for one-, two-, and three-dimensional silver clusters. The numerical results confirm the accuracy and efficiency of the present method.

:In order to perform practical electron correlation calculations, the local unitary transformation (LUT) scheme at the spin-free infinite-order Douglas-Kroll-Hess (IODKH) level [J. Seino and H. Nakai, J. Chem. Phys. 136, 244102 (2012); and ibid. 137, 144101 (2012)], which is based on the locality of relativistic effects, has been combined with the linear-scaling divide-and-conquer (DC)-based Hartree-Fock (HF) and electron correlation methods, such as the second-order Mo̸ller-Plesset (MP2) and the coupled cluster theories with single and double excitations (CCSD). Numerical applications in hydrogen halide molecules, (HX)n (X = F, Cl, Br, and I), coinage metal chain systems, Mn (M = Cu and Ag), and platinum-terminated polyynediyl chain, trans,trans-{(p-CH3C6H4)3P}2(C6H5)Pt(C≡C)4Pt(C6H5){(p-CH3C6H4)3P}2, clarified that the present methods, namely DC-HF, MP2, and CCSD with the LUT-IODKH Hamiltonian, reproduce the results obtained using conventional methods with small computational costs. The combination of both LUT and DC techniques could be the first approach that achieves overall quasi-linear-scaling with a small prefactor for relativistic electron correlation calculations.

The local unitary transformation (LUT) scheme at the spin-free infinite-order Douglas-Kroll-Hess (IODKH) level [J. Seino and H. Nakai, J. Chem. Phys. 136, 244102 (2012)], which is based on the locality of relativistic effects, has been extended to a four-component Dirac-Coulomb Hamiltonian. In the previous study, the LUT scheme was applied only to a one-particle IODKH Hamiltonian with non-relativistic two-electron Coulomb interaction, termed IODKH/C. The current study extends the LUT scheme to a two-particle IODKH Hamiltonian as well as one-particle one, termed IODKH/IODKH, which has been a real bottleneck in numerical calculation. The LUT scheme with the IODKH/IODKH Hamiltonian was numerically assessed in the diatomic molecules HX and X-2 and hydrogen halide molecules, (HX)(n) (X = F, Cl, Br, and I). The total Hartree-Fock energies calculated by the LUT method agree well with conventional IODKH/IODKH results. The computational cost of the LUT method is reduced drastically compared with that of the conventional method. In addition, the LUT method achieves linear-scaling with respect to the system size and a small prefactor. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4757263]

An accurate and efficient scheme for two-component relativistic calculations at the spin-free infinite-order Douglas-Kroll-Hess (IODKH) level is presented. The present scheme, termed local unitary transformation (LUT), is based on the locality of the relativistic effect. Numerical assessments of the LUT scheme were performed in diatomic molecules such as HX and X-2 (X = F, Cl, Br, I, and At) and hydrogen halide clusters, (HX)(n) (X = F, Cl, Br, and I). Total energies obtained by the LUT method agree well with conventional IODKH results. The computational costs of the LUT method are drastically lower than those of conventional methods since in the former there is linear-scaling with respect to the system size and a small prefactor. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4729463]

:The local unitary transformation (LUT) scheme at the spin-free infinite-order Douglas-Kroll-Hess (IODKH) level [J. Seino and H. Nakai, J. Chem. Phys. 136, 244102 (2012)], which is based on the locality of relativistic effects, has been extended to a four-component Dirac-Coulomb Hamiltonian. In the previous study, the LUT scheme was applied only to a one-particle IODKH Hamiltonian with non-relativistic two-electron Coulomb interaction, termed IODKH/C. The current study extends the LUT scheme to a two-particle IODKH Hamiltonian as well as one-particle one, termed IODKH/IODKH, which has been a real bottleneck in numerical calculation. The LUT scheme with the IODKH/IODKH Hamiltonian was numerically assessed in the diatomic molecules HX and X(2) and hydrogen halide molecules, (HX)(n) (X = F, Cl, Br, and I). The total Hartree-Fock energies calculated by the LUT method agree well with conventional IODKH/IODKH results. The computational cost of the LUT method is reduced drastically compared with that of the conventional method. In addition, the LUT method achieves linear-scaling with respect to the system size and a small prefactor.

:An accurate and efficient scheme for two-component relativistic calculations at the spin-free infinite-order Douglas-Kroll-Hess (IODKH) level is presented. The present scheme, termed local unitary transformation (LUT), is based on the locality of the relativistic effect. Numerical assessments of the LUT scheme were performed in diatomic molecules such as HX and X(2) (X = F, Cl, Br, I, and At) and hydrogen halide clusters, (HX)(n) (X = F, Cl, Br, and I). Total energies obtained by the LUT method agree well with conventional IODKH results. The computational costs of the LUT method are drastically lower than those of conventional methods since in the former there is linear-scaling with respect to the system size and a small prefactor.

We presented a two-component relativistic quantum-chemical theory for magnetic shielding constants, which is based on the infinite-order Douglas-Kroll (IODK) transformation. Two-electron relativistic corrections were also generated using the IODK transformation, although negligibly small terms were discarded. The use of small-component basis functions was completely excluded from the present theory. We examined the combination of the levels of relativistic one- and two-electron terms and magnetic interaction terms using the first-order Foldy-Wouthuysen (FW1), the second-order Douglas-Kroll (DK2), and the infinite-order Douglas-Kroll (IODK) transformations, as well as the lowest-order (c(-2)) Breit-Pauli approximation. We calculated the magnetic shielding constants of several closed-shell atoms using the FW1, DK2, IODK, and Breit-Pauli Hamiltonians. The IODK Hamiltonian reproduced well the results calculated by the four-component Dirac-Fock-Coulomb theory: The maximum deviation is only about 2.2%. We found that the accuracy of the magnetic shielding constants is strongly affected by the relativistic treatments of one-electron magnetic interaction, while the effect of the two-component two-electron relativistic corrections is relatively small. We also discussed the picture change effect on magnetic operators. (c) 2010 American Institute of Physics. [doi: 10.1063/1.3413529]

We examined numerically the equivalence between the expectation values calculated by the four-component wave function and those calculated by the two-component wave functions generated by the infinite-order Douglas-Kroll (IODK) transformation. We showed the expectation values &lt; r(-1)&gt; and &lt;delta(r-R)&gt; in several closed-shell atoms using the so-called picture-changed 2 x 2 operators at some levels of approximation. The effect of the two-electron Coulomb term was also discussed. The numerical results indicated that the accuracy of &lt; r(-1)&gt; mainly depends on the level of the wave functions, while that of &lt;delta(r-R)&gt; is affected by the accuracy of both the wave functions and the picture-changed operators. As expected, the picture-changed operators and the IODK wave functions generate essentially equivalent expectation values in comparison with those calculated by the four-component Dirac-type method. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3397070]

We examined the accuracy of two-component quantum-chemical methods, focusing on relativistic treatments of the electron-electron Coulomb interaction. We observed SCF energies, orbital energies, and spin-orbit splittings of He-like and noble-gas atoms up to Uuo (atomic number 118). These were calculated by using either the two-electron term generated by the first-order Foldy-Wouthuysen (2e-FW1) or the infinite-order Douglas-Kroll-Hess (2e-IODKH) transformation, both of which are incorporated with the one-electron terms generated by the IODKH transformation. The 2e-FW1 term was much superior to the lowest-order (c (2)) two-electron Breit-Pauli correction, and the 2e-IODKH term gave energies essentially equivalent to four-component Dirac-Fock/Coulomb energies. (C) 2008 Elsevier B. V. All rights reserved.

The applicability of the lowest-order two-electron Breit-Pauli (2e-BP) relativistic correction incorporated with the infinite-order Foldy-Wouthuysen (IOFW) transformation was examined in heavy and super-heavy elements. Comparing with the non-relativistic Coulomb repulsion term, in cases of moderately heavy noble-gas atoms (He to Ar), the 2e-BP correction gave the SCF energies practically equivalent to those obtained with the Dirac-Fock/Coulomb method. The spin-orbit splittings were also corrected reasonably. On the other hand, in heavy noble-gas atoms (Kr to Rn), the 2e-BP correction tended to overshoot energy lowering, and in a super-heavy atom (E118), evidences of collapse of the 2e-BP correction were observed. (C) 2007 Elsevier B.V. All rights reserved.

Accurate quantum-chemical calculations of the excitation energies and the rotatory strengths of dichalcogens R-Ch-Ch-R(Ch) S, Se, Te) were carried out with the symmetry adapted cluster ( SAC) and SAC-configuration interaction (CI) methods. A series of straight-chain molecules ( dihydrogen dichalcogenide, dimethyl dichalcogenide, and (+)-bis(2-methylbutyl) dichalcogenide) and one cyclic molecule ( 2,3-(R,R)dichalcogenadecalin) were adopted for comparative analysis. The calculated excitation and circular dichroism ( CD) spectra were in good agreement with experimental ones (Laur, P. H. A. In Proceedings of the Third International Symposium on Organic Selenium and Tellurium Compounds; Cagniant, D., Kirsch, G., Eds.; Universite de Metz: Metz, 1979; pp 219-299) within 0.3 eV. The fitting CD spectra also reasonably reproduced the experimental ones. In all the molecules adopted, the first and second lowest bands were assigned to the n-sigma*(Ch-Ch) transition and the third and fourth lowest bands to the n-sigma*(Ch-R) transition. The first and second lowest bands apparently depended on the R-Ch-Ch-R dihedral angle, suggesting that the orbital energies of two sigma*(Ch-Ch) change with the R-Ch-Ch-R dihedral angle. This calculated trend agrees with two empirical rules: the C-2 rule and the quadrant rule.

同位体分別平衡における原子核の体積効果は重原子系で顕著になり、地球化学や宇宙化学の分野で重要である。これまで4成分相対論法に基づく量子化学的手法を用いて、同位体分別係数における核体積項を見積もる研究が行なわれている。4成分法は相対論的に正確であるが計算コストが高く、数原子分子への適応に限られるため、精度を落とさずにより大きな分子が計算できる理論の選定が望まれる。本研究では、4成分法の近似的な相対論法として有力な、Douglas-Kroll (DK) 法に基づく2成分法の精度を検証した。そこでスピン-軌道効果や高次の相対論効果の影響について、4成分法との比較を行った。ウラン分子系において体積効果の計算には、高次のDK変換項とスピン-軌道効果は共に寄与が大きく無視できない。無限次DK法にスピン-軌道効果を適切に考慮した理論を用いることで4成分法とほぼ同精度になり、計算コストを大幅に削減できることを明らかにした。