1P085
解析的微分による化学シフトの相対論的効果の計算(北見工業大学) ○工藤 慶一、福井 洋之<Abstract>
Two expressions for nuclear magnetic shielding tensor components based on analyticallydifferentiating the electronic energy of a system are presented. The first is based on asecond-order Douglas-Kroll-Hess (DKH2) approach, in which the electronic states of thetransformed Dirac Hamiltonian are correct to second order with respect to both the−→nuclear potential V and magnetic vector potential A . The second expression is based on
the method of Barysz-Sadlej-Snijders (BSS), in which the electronic states are completely−→correct with respect to V and correct to second order with respect to A . The two
approaches are applied to the calculation of nuclear magnetic shieldings of hydrogen
halides with common gauge origins. Both methods yield similar results except for theshielding of nucleus I.
<Results and Conclusion>
Two analytical differentiation expressions for calculating nuclear magnetic shielding
tensor components were derived at the coupled Hartree-Fock (CHF) level. The first approach is based on the second-order Douglas-Kroll-Hess (DKH2) method, and the second
approach is based on the method of Barysz-Sadlej-Snijders (BSS). The second method ismore exact than the first method. The two approaches were applied to the calculation ofnuclear magnetic shieldings of hydrogen halides with common gauge origins. Each shielding of halogen and hydrogen atoms was computed using the two common gauge origins
placed at the positions of halogen and hydrogen nuclei. The results are shown in Table
I. The dependence of the computed shieldings on the gauge origin was small enough except for σ iso of the proton in HI. Comparison of the results of present two approaches forhydrogen halide shieldings showed that the relativistic corrections of higher than second
order are negligibly small except for the paramagnetic shielding of the I nucleus. The
present results were found to be consistent with previously reported values for hydrogen
halide shieldings, except for large disorepancies for the anisotropy ∆σ of proton shieldingof HI compared to previous reports. Our calculated BSS-CHF value of ∆σ(H) in HI is26.55ppm (gauge center is on I) while the 4-RPA value of ∆σ(H) in HI is -0.13ppm. The
large anisotropy values for proton shieldings of HI shown in the present calculations are
not thought to be due to error because the present values are similar for the two different
approaches with the two different common geuge origins. Unfortunately, no experimental

values for the anisotropy of proton shielding in HI are available for verification. It is concluded that the present two expressions for calculating nuclear magnetic shielding yieldself-consistent and reliable results.
TABLE I. Calculation of nuclear magnetic shielding constants σ iso (in ppm) for HF, HCl, HBr,and HI by
the DKH2-CHF and BSS-CHF methods.
Molecule
HF

HCl

HBr

HI

Nucleus
FH

Gauge origin
FF

NRa
413.5
28.36

DKH2-CHFb
417.1
26.92

BSS-CHFc
417.0
26.92

4-RPAd
423.3
27.87

FH

H
H

413.5
28.36

412.6
26.73

412.6
26.73

423.3
27.87

ClH

Cl
Cl

949.9
30.65

988.3
30.51

987.8
30.51

1020.1
31.00

ClH

H
H

949.9
30.65

983.3
30.09

982.8
30.09

1020.1
31.00

Br
H

Br
Br

2641.331.01

2982.135.45

2972.235.46

3224.636.08BrHHH

2641.331.01

2978.635.61

2968.735.62

3224.636.08

IHII

4539.831.20

6303.444.18

6244.944.20

6768.4
47.98

IH

H
H

4539.831.20

6301.145.77

6242.745.80

6768.447.98

a Previous nonrelativistic results using GIAO’s.

H. Fukui and T. Baba, J. Chem. Phys. 117, 7836 (2002).
b Present DKH2-CHF results.
c Present BSS-CHF results.
d Four-component relativistic random phase approximation results using GIAOs.

L. Visscher, T. Enevoldsen, T. Saue, H. J. Aa. Jensen, and J. Oddershede, J. Comput. Chem.
20, 1262 (1999).