同位体置換による 核磁気共鳴化学シフトの理論的研究 Theoretical Study of Nuclear Magnetic Resonance Chemical Shift Induced by Isotope Effect ○杉森公一, 川辺弘之 Kimikazu SUGIMORI, Hiroyuki KAWABE 金城大学社会福祉学部 3/13/2022 1 日本化学会第９０回春季年会 21A 口頭B講演

Isotope effect in chemistry • Kinetic Isotope Effect (KIE) • Geometrical Isotope Effect (GIE) • H/D isotope effect o Intra-, inter-hydrogen bonding o Nuclear Magnetic Resonance (NMR) o Additivity, primary/secondary isotope shift 3/13/2022 日本化学会第９０回春季年会 1H9-28 2 Geometrical change  Molecular properties

Nuclear magnetic shielding in H/D isotope effect • Nuclear shielding at equilibrium distance • At finite temperature  zero-point vibration, nuclear mass-dependency 3/13/2022 日本化学会第９０回春季年会 1H9-28 3 X H X D = X H X D ≠ e- e- deshielding shielding Re Re >

Nuclear mass-dependent theory & calculation(1) • Path-integral quantum Monte Carlo (PIMC) o M.C. Böhm et al., Chem. Phys. Lett. 322, 117 (2000). o J. Schulte et al., Mol. Phys. 99, 1155-1158 (2001). • Nuclear/Molecular Orbital method o S. Webb et al., J. Chem. Phys. 117,4106-4118 (2002). o H. Nakai, Int. J. Quantum Chem. 86, 511-517 (2002). o M. Tachikawa, Chem. Phys. Lett. 360, 494-500 (2002). For NMR property o Y. Kita, et al., J. Mol. Struct. (THEOCHEM) 912, 2-4 (2009). 3/13/2022 日本化学会第９０回春季年会 1H9-28 4

Nuclear mass-dependent theory & calculation(2) • Empirical model o T. W. Marshall, Mol. Phys. 3, 61-63 (1961). o A. D. Buchkingham, J. Chem. Phys. 36, 3096 (1962). • VSCF, anharmonic vibrational correction o P.-O. Åstrand et al., J. Chem. Phys. 112, 2655-2667 (2000). • Based on PES o A. C. de Dios et al., Annu. Rep. NMR Spectrosc. 29, 1-69 (1994). o R. D. Wigglesworth et al., J. Chem. Phys. 112, 736-746 (2000). 3/13/2022 日本化学会第９０回春季年会 1H9-28 5

Born-Oppenheimer Approx. Nuclear-fixed and unfixed Equilibrium vs. Average 3/13/2022 日本化学会第９０回春季年会 21A 口頭 B講演 6 Schrödinger Non-BO PIMC NMO BO PES VSCF

Theory: BO & PES 3/13/2022 日本化学会第９０回春季年会 21A 口頭 B講演 7     R r R R r ; ) ( ; elec n n n U H        R R R nm nm nm n E U T     )) ( ( N     R R R R vib vib vib )) ( ) ( (   E U T   Rotation and transition-free case   R r R R r ; ) ( ) , ( n     Under Born-Oppenheimer approximation, nuclear wavefunction is depended on adiabatic potential U.

Theory: Morse oscillator • Morse potential as adiabatic potential 3/13/2022 日本化学会第９０回春季年会 1H9-28 8      2 M 1 e R R e e D R V      2 2 2 2 2 1 2 2            v D D E e e v       • Energy level & wavefunction in analytical form ) ( ) ( ) ( 2 2 z L z e z b v b z v    3 parameters Fully analytical solution with Laguerre polynomial

Theory: Thermal average • Boltzmann’s distribution at finite temperature T. 3/13/2022 日本化学会第９０回春季年会 1H9-28 9        v v v u T k E v v v T k E T R n e R R e R u v B B / / ) ( ) (              v v v u T k E v v v T k E T R n e R R e u v      B B / / ) ( ) ( n = 0 at 0 K

Procedure 1. Potential energy surface(PES) / Magnetic shielding surface(MSS) by MO/DF method 2. Determining Morse Parameters , De , Re 3. Solving Morse wavefunctions and averaged Reff = 4. Thermal average at finite temperature at T 5. Magnetic shielding constant at RT eff 6. Primary isotope shift: 1D = XD - XH 3/13/2022 日本化学会第９０回春季年会 1H9-28 10 ) ( ) ( R R R v v v   

Computational details • PES o UHF / aug-cc-pVTZ Gaussian 03 Rev.E01 o UMP2 / aug-cc-pVTZ Gaussian 03 Rev.E01 o UCCSD / aug-cc-pVTZ CFour ver.1.2 (beta/rc) o UB3LYP / aug-cc-pVTZ Gaussian 03 Rev.E01 o UPBE1PBE / aug-cc-pVTZ Gaussian 03 Rev.E01 • Morse wavefunction o Analytical function solved in Discrete Variable Representation (DVR) of 0.0001 a.u. (0.1 mBohr) grid. • Nuclear magnetic shielding constant o Gauge-Independent Atomic Orbital (GIAO) method 3/13/2022 日本化学会第９０回春季年会 1H9-28 11

Target molecules • Homo nucleic diatomic molecule: • Hetero nucleic diatomic molecule: 3/13/2022 日本化学会第９０回春季年会 1H9-28 12 H H(D) H(D) Cl Na H(D) 1H-NMR 1H-NMR, 1H-NMR, 35Cl-NMR 23Na-NMR

PES & MSS (1H-NMR for H2 ) Hydrogen molecule 3/13/2022 日本化学会第９０回春季年会 21A 口頭 B講演 13 PES UHF UMP2 UB3LYP UCCSD MSS deshielding

PES & MSS (1H-NMR for HCl) Hydrogen chloride molecule 3/13/2022 日本化学会第９０回春季年会 21A 口頭 B講演 14 UHF UMP2 UB3LYP UCCSD UPBE1PBE PES MSS deshielding 1S 0.139 2S 0.380 3S 0.227 1S 0.250 2S 0.435 3S 0.041

PES & MSS (35Cl-NMR for HCl) Hydrogen chloride molecule 3/13/2022 日本化学会第９０回春季年会 21A 口頭 B講演 15 PES MSS deshielding 2S 1.873 3S 1.170 4S 0.257 5S 0.678 2S 1.868 3S 1.134 4S 0.254 5S 0.672

PES & MSS (1H-NMR for NaH) Sodium hydride molecule 3/13/2022 日本化学会第９０回春季年会 21A 口頭 B講演 16 PES MSS UHF UMP2 UB3LYP UCCSD UPBE1PBE deshielding

PES & MSS (23Na-NMR for NaH) Sodium hydride molecule 3/13/2022 日本化学会第９０回春季年会 21A 口頭 B講演 17 PES MSS shielding

Thermal averaged vs. Equilibrium Re by using B3LYP parameterization 3/13/2022 日本化学会第９０回春季年会 1H9-28 18

Thermal averaged T() and Equilibrium (Re ) by using GIAO/B3LYP and CCSD method 3/13/2022 日本化学会第９０回春季年会 1H9-28 19 Exp. 0.038 GIAO/B3LYP GIAO/CCSD

Summary • PES and MSS o Shapes of PES are not quite different without HF/aug-cc-pVTZ results which shows underestimated dissociation energy.  MP2 and hybrid DFT are effective for PES. o MSS behaviors represents the feature of shielding around the equilibrium distance. Deshielding or shielding characters are depended on the dissociation state. • GIE and Isotope shift by Morse wavefunction o By using Morse oscillator, isotope effect of H/D are obtained with low computational cost and effective. o B3LYP and CCSD results of shielding constant are quite close within the range of ppm~ppb. 3/13/2022 日本化学会第９０回春季年会 1H9-28 20

Concluding remarks • Application: o Polyatomic molecule o Primary and secondary isotope shift with respect to 13C chemical shift. • Another degree of freedom o Bending vibration, torsional vibration, ...  Extended Morse potentials. o Rotational mode  Dunham potential. 3/13/2022 日本化学会第９０回春季年会 1H9-28 21

Acknowledgement • Author thanks o Dr. Hideto SHIMAHARA (JAIST) o Dr. Taku MIZUKAMI (JAIST) o Prof. Hidemi NAGAO (Kanazawa Univ.) o Prof. Kiyoshi NISHIKAWA (Kanazawa Univ.) • This work is supported by JSPS KAKENHI, Grant-in-Aid for Encouragement of Scientists 科学研究費補助金（奨励研究） (21915007) 「同位体置換による核磁気共鳴化学シフトの変化に関する 理論的研究」. 3/13/2022 日本化学会第９０回春季年会 1H9-28 22

Tables(1) 3/13/2022 日本化学会第９０回春季年会 1H9-28 23 Table 1: Morse parameters determined by using B3LYP/aug-cc-pVTZ. Table 2: Equilibrium internuclear distance Re , average internuclear distance of hydrogen-isotope, of deuterated isotope, and their ratio to Re , in ångström.

Tables(2) 3/13/2022 日本化学会第９０回春季年会 1H9-28 24 Table 4: Calculated NMR-GIAO shielding tensor σ (isotropic value) in ppm of the equilibrium internuclear distance Re , average internuclear distance T of hydrogen-isotope, T of deuterated isotope, and their ratio to Re . Table 3: Isotope shift of internuclear distance and T.