Director, Quantum Chemistry Research Institute (QCRI)
Visiting Professor, Waseda University
Professor Emeritus, Kyoto University
Email:h.nakatsuji/a/qcri.or.jp (replace /a/ with @)
WWW: http://www.qcri.or.jp/?lang=en
Tel: -81-75-634-3211 Fax: -81-75-634-3211
Address: Quantum Chemistry Research Institute
Kyoto Technoscience Center 16, 14 Yoshida-Kawara-Machi, Sakyou-Ku, Kyoto 606-8305, Japan
1) Deepening and Extending the Quantum Principles in Chemistry, H. Nakatsuji, Bull. Chem. Soc. Jap. 78, 1705 (2005).
2) P. A. M. Dirac, Proc. Roy. Soc. (London), A123, 714 (1929).
3) H. Eyring, J. Walter, G. E. Kimball, "Quantum Chemistry", John Wiley & Sons, Inc., New York (1944).
4) Structure of the Exact Wave Function, H. Nakatsuji, J. Chem. Phys., 113, 2949-2956 (2000).
5) Structure of the Exact Wave Function. H. Nakatsuji and E. R. Davidson, II. Iterative Configuration Interaction Method, J. Chem. Phys. 115, 2000-2006 (2001).
6) Structure of the Exact Wave Function. III. Exponential Ansatz, H. Nakatsuji, J. Chem. Phys., 115, 2465-2475 (2001).
7) Structure of the Exact Wave Function. IV. Excited Sates from Exponential Ansatz and Comparative Calculations by the Iterative Configuration Interaction and Extended Coupled Cluster Theories, H. Nakatsuji, J. Chem. Phys., 116, 1811-1824 (2002)
8) Structure of the Exact Wave Function. V. Iterative Configuration Interaction Method for Molecular Systems within Finite Basis, H. Nakatsuji and M. Ehara, J. Chem. Phys., 117, 9-12 (2002).
9) Inverse Schrödinger Equation and the Exact Wave Function, H. Nakatsuji, Phys. Rev. A 65, 052122 (2002).
10) Scaled Schrödinger Equation and the Exact Wave Function, H. Nakatsuji, Phys. Rev. Lett. 93, 030403 (2004).
11) General Method of Solving the Schrödinger Equation of Atoms and Molecules, H. Nakatsuji, Phys. Rev. A, 72, 062110 (2005).
12) Free ICI (Iterative Complements Interaction) Calculations of Hydrogen Molecule, Y. Kurokawa, H. Nakashima, and H. Nakatsuji, Phys. Rev. A, 72, 062502 (2005).
13) Analytically Solving the Dirac-Coulomb Equation for Atoms and Molecules, H. Nakatsuji and H. Nakashima, Phys. Rev. Lett., 95, 050407 (2005).
14) Iterative CI General Singles and Doubles (ICIGSD) Method for Calculating the Exact Wave Functions of the Ground and Excited States of Molecules, H. Nakatsuji, M. Ehara, J. Chem. Phys. 112, 194108 (2005).
15) Solving the Schrödinger Equation for Helium Atom and Its Isoelectronic Ions with the Free Iterative Complement Interaction (ICI) Method, H. Nakashima, H. Nakatsuji, J. Chem. Phys. 127, 224104 (2007).
16) Solving the Schrödinger Equation of Atoms and Molecules without Analytical Integration Based on the Free Iterative-Complement-Interaction Wave Function" H. Nakatsuji, H. Nakashima, Y. Kurokawa, A. Ishikawa, Phys. Rev. Lett, 99, 240402 (2007).
17) Solving the Electron-Nuclear Schrödinger Equation of Helium Atom and Its Isoelectronic Ions with the Free Iterative-Complement-Interaction Method, H. Nakashima and H. Nakatsuji, J. Chem. Phys. 128, 154108 (2008).
18) Solving the Electron and Electron-Nuclear Schrödinger Equations for the Excited States of Helium Atom with the Free Iterative-Complement-Interaction Method, H. Nakashima, Y. Hijikata and H. Nakatsuji, J. Chem. Phys. 128, 154108 (2008).
19) Solving the Schrödinger and Dirac Equations of Hydrogen Molecular Ion Accurately by the Free Iterative Complement Interaction Method, A. Ishikawa, H. Nakashima, and H. Nakatsuji, J. Chem. Phys. 128, 124103-1-12 (2008).
20) Solving the Schrödinger Equation of Helium and Its Isoelectronic Ions with the Exponential Integral (Ei) Function in the Free Iterative Complement Interaction Method, Y. I. Kurokawa, H. Nakashima, and H. Nakatsuji, Phys. Chem. Chem. Phys. 10, 4486 (2008).
21) How accurately does the free complement wave function of a helium atom satisfy the Schrödinger equation? H. Nakashima and H. Nakatsuji, Phys. Rev. Lett. 101, 240406-1-4 (2008).
22) R. N. Hill and C. Krauthauser, Phys. Rev. Lett. 58, 83 (1987).
II. SAC/SAC-CI Method for Studying Chemistries of Excited and Ionized States [*]
1. Single-reference theory
Nakatsuji and Hirao proposed the SAC (symmetry adapted cluster) method for the ground states of closed and open-shell electronic structures [1-3]. The SAC method is a kind of coupled cluster method that takes all the excitation operators to be symmetry adapted, so that no spin-contamination problem arises and it leads to a stable convergence to the spin-eigen function. Then, Nakatsuji proposed in 1978 the SAC-CI (configuration interaction) method [4-6] to describe accurately and efficiently the electronic structures of the excited, ionized and electron-attached states of molecules (ground and excited states of singlet to triplet spin multiplicities). The coding of the SAC/SAC-CI method was completed in singles and doubles approximation for all of these states in the same year and applied to water et cetera to examine the accuracy of the method. In those days, no full-CI calculations existed and only SDTQ CI results were available for water with very limited basis set, but the SAC/SAC-CI results were satisfactorily quite accurate, reproducing these SDTQ-CI results for both ground and excited states. Outside Japan, a CCD coding was reported by John Pople around this year [7], but the SAC/SAC-CI theory and coding [1-6] correspond to the CCSD[8]/CCLRT[9] or EOM-CC[10] theory. But, such codes were developed much later in the West World.
The SAC/SAC-CI method was applied to the valence and Rydberg singlet and triplet excitations and the ionization of various molecules from small to relatively large molecules like porphyrins and gave very accurate descriptions of these various electronic states [11-13]. The methods were also used to study the inner-valence ionization spectra and their satellites [13], the excitation and ionization spectra and the hyper-fine splitting constants of radicals [14]. These studies opened a reliable ab initio methodology for studying excited, ionized, and open-shell molecules with the SAC-CI calculations.
The original SAC-CI code was for ordinary single-electron excited or ionized states (SAC-CI SD-R), but it was extended later to multi-electron excitation and ionization (shake-up) states (SAC-CI general-R) [15] and further to include high-spin electronic states of quartet-to-septet spin multiplicities [16]. The accuracy of the SAC/SAC-CI method was confirmed by comparing the results with the experimental results and also with the full-CI results when they were available [17,18]. The geometries of the excited states and the courses of the photochemical reactions are studied efficiently when the forces acting on the constituent nuclei of the systems are available. For this purpose, the energy gradient method was implemented in the SAC/SAC-CI code [19,20], so that we can calculate the forces acting on the constituent nuclei for every ground and excited state of singlet to septet spin-multiplicities of both single and multi-electron excitation natures. This enables us to calculate the geometries of molecules in excited and ionized states and to study the dynamics of molecular systems in their ground, excited and ionized states, which are difficult to study by experimental methods alone.
The SAC/SAC-CI method was implemented in Gaussian 03 in the spring of 2003 and is now widely used worldwide not only in universities and institutes, but also in industries. The improvements and the extensions of the SAC/SAC-CI code on Gaussian are consistently done in our laboratory to explore the SAC-CI world in chemistry. The method has been applied in our laboratory to various chemistries involving more than 170 molecules in the ground and excited states of organic, inorganic, and surface molecular systems. The SAC-CI methodology related with Gaussian is summarized in the WEB [21].
The SAC/SAC-CI method is applicable to the ground, excited, ionized, and electron-attached states of valence, Rydberg, inner-valence, and inner-core energy regions in a same good accuracy and therefore has opened a new field called theoretical fine spectroscopy, which in conjunction with the experimental fine spectroscopy, opens a new dimension of spectroscopy and dynamics in chemistry [22-24]. By calculating the potential energy surfaces of the ground, excited and ionized states, fine vibrational structures of the spectra are also studied by the SAC-CI method. This is true not only for the main excitation and ionization peaks, but also for many satellite peaks accompanying to the main peaks, which are due to multi-electron processes. The open-reference (OR-)SAC/SAC-CI method has recently been developed and used to study efficiently the inner-core excitations and their satellites [25].
The SAC-CI methodology has made it also applicable to relatively large molecules like porphyrins and biologically important molecular systems. So, this method is very useful for the study of photo-biology. For example, the spectra and the electron transfer pathways of the photosynthetic reaction centers of Rhodopseudomonas Viridis [26-28] and Rhodobactor Sphaeroides [29], photosynthetic bacteria, were clarified with this method. In combination with the QM/MM method where QM is SAC-CI, this method has been very powerful for studying the color tuning mechanism in retinal proteins [30]. Similar approach is also possible by using the SAC-CI/ONIOM method recently incorporated in Gaussian [31].
Surface photochemistry is also an interesting field to which the SAC-CI method has been applied. With the help of the Dipped Adcluster Model (DAM) explained below, we can describe the electronic structures of molecules adsorbed on a metal surface [32,33]. Large low-field shifts of the spectra of the adsorbates in comparison with the gas-phase spectra are well described by a combination of the DAM and the SAC-CI method. By combining the experimental and SAC-CI theoretical surface spectroscopies, we can not only identify the adsorbate species, but also clarify the electronic structures of the adsorbates, for which experiments alone are very difficult in reality. More details will be explained below together with the DAM.
The direct algorithm was introduced recently to accelerate the calculations and to increase the accuracy of the SAC and SAC-CI program [34]. So far, the direct algorithm was introduced only to the singles and doubles part, and the introduction to the general R part is in progress.
Extensions of the SAC/SAC-CI methodology to truly giant molecular systems such as molecular crystals, polymers, and biological systems are important for investigating photo-electronic processes in giant molecular systems. Giant SAC/SAC-CI theory and its code have been completed recently [35], realizing the study of giant molecular systems without loss of accuracy. In such a giant systems, exact satisfaction of the size extensivity and the size intensivity are important, because if not satisfied, the error soon becomes incredible. Interesting applications are now in progress.
*http://qcri.or.jp/sacci/
1) Cluster Expansion of the Wavefunction. Pseudo-Orbital Theory Applied to Spin Correlation, H. Nakatsuji and K. Hirao, Chem. Phys. Lett., 47(3), 569-571 (1977).
2) Cluster Expansion of the Wavefunction. Symmetry-Adapted-Cluster (SAC) Expansion, Its Variational Determination, and Extension of Open-Shell Orbital Theory, H. Nakatsuji and K. Hirao, J. Chem. Phys., 68(5), 2053-2065 (1978).
3) Cluster Expansion of the Wavefunction. Pseudo-Orbital Theory Based on the SAC Expansion and Its Application to the Spin Density of Open-Shell Systems, H. Nakatsuji and K. Hirao, J. Chem. Phys., 68(9), 4279-4291 (1978).
4) Cluster Expansion of the Wavefunction. Excited States, H. Nakatsuji, Chem. Phys. Lett., 59(2), 362-364 (1978).
5) Cluster Expansion of the Wavefunction. Electron Correlations in Ground and Excited States by SAC (Symmetry-Adapted-Cluster) and SAC-CI Theories, H. Nakatsuji, Chem. Phys. Lett., 67(2,3), 329-333 (1979).
6) Cluster Expansion of the Wavefunction. Calculation of Electron Correlations in Ground and Excited States by SAC and SAC-CI Theories, H. Nakatsuji, Chem. Phys. Lett., 67(2,3), 334-342 (1979).
7) J. A. Pople, R. Krishnan, H. B. Schlegel and J. S. Binkley, Int. J. Quantum Chem. 14, 545 (1978).
8) G. D. Purvis and R. J. Bartlett, J. Chem. Phys. 76, 1910 (1982).
9) H. Koch and P. Jørgensen, J. Chem. Phys., 93, 3333 (1990).
10) J. F. Stanton and R. J. Bartlett, J. Chem. Phys., 98, 7029. (1993)
11) Electronic Structures of Ground, Excited, Ionized, and Anion States Studied by the SAC/SAC-CI Theory, H. Nakatsuji, Acta Chimica Hungarica, Models in Chemistry, 129(5), pp.719-776 (1992).
12) SAC-CI Method: Theoretical Aspects and Some Recent Topics, H. Nakatsuji, in Computational Chemistry - Reviews of Current Trends, Vol. 2, p. 62-124 (1997).
13) Cluster Expansion of the Wavefunction. Valence and Rydberg Excitations, Ionizations, and Inner-Valence Ionizations of CO2 and N2O Studied by the SAC and SAC-CI Theories, H. Nakatsuji, Chem. Phys., 75, 425 (1983)
14) Cluster Expansion of the Wavefunction. Spin and Electron Correlations in Doublet Radicals Studied by the SAC and SAC-CI Theories, H. Nakatsuji, K. Ohta, and T. Yonezawa, J. Phys. Chem., 87, 3068 (1983).
15) Description of Two- and Many-Electron Processes by the SAC-CI Method, H. Nakatsuji, Chem. Phys. Lett., 177(3), 331-337 (1991).
16) SAC-CI Method Applied to High-Spin Multiplicity, H. Nakatsuji and M. Ehara, J. Chem. Phys., 98(9), 7179-7184 (1993).
17) SAC-CI and Full CI Calculations for the Singlet and Triplet Excited States of H2O, H. Nakatsuji, K. Hirao, and Y. Mizukami, Chem. Phys. Lett., 179(5,6), 555-558 (1991).
18) Outer- and Inner-Valence Ionization Spectra of N2 and CO: SAC-CI (general-R) Spectra Compared with the Full-CI One, M. Ehara and H. Nakatsuji, Chem. Phys. Lett., 282(5,6) 347-354 (1998).
19) Analytical Energy Gradient of the Ground, Excited, Ionized and Electron-Attached States Calculated by the SAC/SAC-CI Method, T. Nakajima and H. Nakatsuji, Chem. Phys. Lett., 280 (1,2) 79-84 (1997).
20) Analytical Energy Gradients of the Excited, Ionized and Electron-Attached States Calculated by the SAC-CI General-R Method, M. Ishida, K. Toyoda, M. Ehara and H. Nakatsuji, Chem. Phys. Lett., 347, 493-498 (2001).
21) http://qcri.or.jp/sacci/
22) SAC-CI General-R Study of the Ionization Spectrum of HCl, M. Ehara, P. Tomasello, J. Hasegawa, and H. Nakatsuji, Theor. Chem. Acc., 102 (1-6), 161-164 (1999).
23) Electronic Excitation Spectra of Furan and Pyrolle: Revisit by the SAC-CI Method, J. Wan, J. Meller, M. Hada, M. Ehara, and H. Nakatsuji, J. Chem. Phys., 113(18), 7853-7866 (2000).
24) Fine Theoretical Spectroscopy Using SAC-CI General-R Method: Outer- and Inner-Valance Ionization Spectra of CS2 and OCS, M. Ehara, M. Ishida, and H. Nakatsuji, J. Chem. Phys., 117, 3248-3255 (2002).
25) Inner-shell ionizations and satellites studied by the OR-SAC/SAC-CI method Y. Ohtsuka and H. Nakatsuji, J. Chem. Phys. in press.
26) Excited States and Electron Transfer Mechanism in the Photosynthetic Reaction Center of Rhodopseudomonas Viridis: SAC-CI Study, H. Nakatsuji, J. Hasegawa, and K. Ohkawa, Chem. Phys. Lett., 296 (5,6), 499-504 (1998).
27) Excited States of the Photosynthetic Reaction Center of Rhodopseudomonas Viridis: SAC-CI Study, J. Hasegawa, K. Ohkawa, H. Nakatsuji, J. Phys. Chem. B, 102 (50), 10410-10419 (1998).
28) Mechanism and Unidirectionality of the Electron Transfer in the Photosynthetic Reaction Center of Rhodopseudomonas Viridis: SAC-CI Theoretical Study, J. Hasegawa and H. Nakatsuji, J. Phys. Chem. B, 102 (50), 10420-10430 (1998).
29) Mechanism and Excited States and Electron Transfer Mechanism in the Photosynthetic Reaction Center of Rhodobactor Sphaeroides: SAC-CI Theoretical Study, J. Hasegawa and H. Nakatsuji, Chemistry Letters. 34, 1242-1243 (2005).
30) Mechanism of color-tuning in retinal proteins: SAC-CI and QM/MM study, K. Fujimoto, J. Hasegawa, S. Hayashi, S. Kato, H. Nakatsuji, Chem. Phys. Lett., 414, 239-242 (2005).
31) Y. Ohtuka, H. Nakatsuji, and K. Morokuma, Symposium on Molecular Science, 2P098, Tokyo, Sept. 27-30, 2005.
32) Dipped Adcluster Model for Chemisorptions and Catalytic Reactions on a Metal Surface, H. Nakatsuji, J. Chem. Phys., 87(8), 4995-5001 (1987).
33) Dipped Adcluster Model for Chemisorption and Catalytic Reactions, H. Nakatsuji, Progress in Surface Science, Vol. 54, p. 1-68 (1997).
34) Formulation and Implementation of the Direct Algorithm for the SAC/SAC|CI Method, J. Chem. Phys. 128, 094105-1-14 (2008).
35) SAC/SAC-CI Methodology extended to Giant Molecular Systems: Ring Molecular Crystals, H. Nakatsuji, T. Miyahara and R. Fukuda, J. Chem. Phys. 126, 084105-1-18 (2007).
1) Multireference Cluster Expansion Theory: MR-SAC Theory, H. Nakatsuji, J. Chem. Phys., 83, 713-722 (1985).
2) Exponentially Generated Wave Functions, H. Nakatsuji, J. Chem. Phys., 83(11), 5743-5748 (1985).
3) Exponentially Generated Configuration Interaction Theory. Descriptions of Excited, Ionized, and Electron Attached States, H. Nakatsuji, J. Chem. Phys., 94(10), 6716-6727 (1991).
4) Mixed-Exponentially Generated Wave Function Method for Ground, Excited, Ionized, and Electron Attached States of a Molecule, H. Nakatsuji, J. Chem. Phys., 95(6), 4296-4305 (1991).
5) EGCI Method Applied to High-Spin Multiplicity, H. Nakatsuji and M. Ehara, J. Chem. Phys., 99(3), 1952-1961 (1993).
6) Exponentially Generated Wave Functions and Excited States of Benzene, H. Nakatsuji, Theoret. Chim. Acta., 71(2,3), 201-229 (1987).
1) Equation for the Direct Determination of the Density Matrix, H. Nakatsuji, Phys. Rev., A14, 41 (1976).
2) Equation for the Direct Determination of the Density Matrix: Time- Dependent Density Equation and Perturbation Theory, H. Nakatsuji, Theor. Chem. Acc. 102, 97-104 (1999).
3) C. Valdemoro, Phys. Rev. A 45, 4462 (1992).
4) Direct Determination of the Quantum-Mechanical Density Matrix Using the Density Equation, H. Nakatsuji and K. Yasuda, Phys. Rev. Lett., 76, 1039-1042 (1996).
5) Direct Determination of the Quantum-Mechanical Density Matrix Using the Density Equation. II., K. Yasuda and H. Nakatsuji, Phys. Rev. A 56, 2648-2657 (1997).
6) Density Equation Theory in Chemical Physics, H. Nakatsuji, in Many-electron Densities and Reduced Density Matrices, edited by J. Cioslowski, Kluwer Academic, New York 2000, pp85-116.
7) Variational Calculations of Fermion Second-Order Reduced Density Matrices by Semi- definite Programming Algorithm, M. Nakata, H. Nakatsuji, M. Ehara, M. Fukuda, K. Nakata, and K. Fujisawa, J. Chem. Phys., 114, 8282-8292 (2001).
8) Density Matrix Varitional Theory: Application to the Potential Energy Surfaces and Strongly Correlated Systems, M. Nakata, M. Ehara, and H. Nakatsuji, J. Chem. Phys., 116, 5432-5439 (2002).
1) Dipped Adcluster Model for Chemisorptions and Catalytic Reactions on a Metal Surface, H. Nakatsuji, J. Chem. Phys., 87(8), 4995-5001 (1987).
2) Dipped Adcluster Model for Chemisorptions and Catalytic Reactions on a Metal Surface: Image Force Correction and Applications to Pd-O2 Adclusters, H. Nakatsuji, H. Nakai, and Y. Fukunishi, J. Chem. Phys., 95(1), 640-647 (1991).
3) Theoretical Model Studies for Surface-Molecule Interacting Systems, H. Nakatsuji, Intern. J. Quantum Chem., Symp.26, 725-736 (1992).
4) Dipped Adcluster Model for Chemisorption and Catalytic Reactions, H. Nakatsuji, Progress in Surface Science, Vol. 54, p. 1-68 (1997).
5) Theoretical Study on Molecular and Dissociative Chemisorptions of an O2 Molecule on an Ag Surface:Dipped Adcluster Model Combined with SAC-CI Method, H. Nakatsuji and H. Nakai, Chem. Phys. Lett., 174(3,4), 283 (1990).
6) Dipped Adcluster Model Study for Molecular and Dissociative Chemisorption of O2 on an Ag Surface, H. Nakatsuji and H. Nakai, J. Chem. Phys. 98(3), 2423-2436 (1993).
7) Mechanism of the Partial Oxidation of Ethylene on an Ag Surface: Dipped Adcluster Model Study, H. Nakatsuji, K. Ikeda, Y. Yamamoto, and H. Nakai, Surf. Sci., 384, 315-333 (1997).
8) Theoretical Studies on the Catalytic Activity of Ag Surface for the Oxidation of Olefins, H. Nakatsuji, Z. M. Hu, and H. Nakai, Intern. J. Quantum. Chem., 65, 839-855 (1997).
9) Electron Transfer and Back-Transfer in the Partial Oxidation of Ethylene on an Ag Surface: Dipped Adcluster Model Study, H. Nakatsuji, K. Takahashi, and Z.M Hu, Chem. Phys. Lett., 277(5,6), 551-557 (1997).
10) Activation of O2 on Cu, Ag, and Au Surfaces for the Epoxidation of Ethylene: Dipped Adcluster Model Study, H. Nakatsuji, Z. M. Hu, H. Nakai and K. Ikeda, Surf. Sci., 387 328-341 (1997)
11) Oxidation Mechanism of Propylene on an Ag Surface: Dipped Adcluster Model Study, Z. Hu, H. Nakai, and H. Nakatsuji, Surf. Sci., 401(3), 371-391 (1998).
12) Active Sites for Methanol Synthesis on a Zn/Cu(100) Catalyst, Z. M. Hu, and H. Nakatsuji, Chem. Phys. Lett., 313 (1,2), 14-18 (1999).
13) Mechanism of the Hydrogenation of CO2 to Methanol on a Cu(100) Surface: Dipped Adcluster Model Study, Z. M. Hu, K. Takahashi, and H. Nakatsuji, Sur. Sci., 442,(1), 90-106 (1999).
14) Mechanism of Methanol Synthesis on Cu(100) and Zn/Cu(100) Surfaces: Comparative Dipped Adcluster Model Study, H. Nakatsuji and Zhen-Ming Hu, Intern. J. Quantum Chem., 77, 341-349 (2000).
15) Dipped Adcluster Model and SAC-CI Method Applied to Harpooning, Chemiluminescence, and Electron Emission in Halogen Chemisorption on Alkali Metal Surface, H. Nakatsuji, R. Kuwano, H. Morita and H. Nakai, J. Mol. Catalysis, 82, 211-228 (1993).
16) Theoretical Surface Spectroscopy of NO on the Pt(111) Surface with the DAM (Dipped Adcluster Model) and the SAC-CI Method, H. Nakatsuji, N. Matsumune, and K. Kuramoto, J. Chem. Theo. Comp. 1, 239-247 (2005).
1) Theoretical Study of the Metal Chemical Shift in Nuclear Magnetic Resonance. Ag, Cd, Cu, and Zn Complexes, H. Nakatsuji, K. Kanda, K. Endo, and T. Yonezawa, J. Am. Chem. Soc., 106, 4653 (1984).
2) Electronic Mechanisms of Metal Chemical Shifts from Ab Initio Theory, H. Nakatsuji, in Nuclear Magnetic Shieldings and Molecular Structure, Ed. by J. A. Tossell, NATO ASI Series, C386, Reidel, Dordrecht, pp. 263-278 (1993).
3) Spin-Orbit Effect on the Magnetic Shielding Constant Using Ab Initio UHF Method, H. Nakatsuji, H. Takashima, and M. Hada, Chem. Phys. Lett., 233, 95-101 (1995).
4) Relativistic Study of Nuclear Magnetic Shielding Constants: Hydrogen Halides, C. C. Ballard, M. Hada, H. Kaneko, and H. Nakatsuji, Chem. Phys. Lett., 254, 170-178 (1996).
5) Relativistic Configuration Interaction and Coupled Cluster Methods Using Four-Component Spinors: Magnetic Shielding Constants of HX and CH3X (X = F, Cl, Br, I), M. Kato, M. Hada, R. Fukuda, H. Nakatsuji, Chem. Phys. Lett., 408, 150-156 (2005)
1) Electrostatic Force Theory for a Molecule and Interacting Molecules I. Concept and Illustrative Applications, H. Nakatsuji, J. Am. Chem. Soc., 95(2), 345 (1973).
2) Force Models for Molecular Geometry, H. Nakatsuji and T. Koga, in The Force Concept in Chemistry, B. M. Deb, Ed. (Van Nostrand Reinhold, New York,1981), Chap.3, pp. 137-217.
3) Common Natures of the Electron Cloud of the System Undergoing Change in Nuclear Configuration, H. Nakatsuji, J. Am. Chem. Soc., 96(1), 24 (1974).
4) Force in SCF Theories, H. Nakatsuji, K. Kanda, and T. Yonezawa, Chem. Phys. Lett., 75(2), 340 (1980).
5) Force in SCF Theories. Second Derivative of Potential Energy, H. Nakatsuji, K. Kanda, and T. Yonezawa, J. Chem. Phys., 77, 1961 (1982).