Calculation of Nuclear Magnetic Shielding in Hydrogen Molecule

Abstract

The variation method for the calculation of nuclear magnetic shielding as described by Das and Bersohn [Phys. Rev. 104, 849 (1956)] has been shown to be justified on the basis of Rebane's [Soviet Phys.‐JETP 11, 694 (1960)] more general considerations. This variation method has been employed to recalculate the proton magnetic shielding in the hydrogen molecule. The vector potential for the externally applied uniform magnetic field H is taken in the following form: $${\mathbf{A}}_{\mathrm{xx}}\text{≡(0,0,yH);\hspace{0.17em}\hspace{0.17em}}{\mathbf{A}}_{\mathrm{yy}}\text{≡(0,0,−xH);\hspace{0.17em}\hspace{0.17em}}\mathrm{and}\hspace{0.17em}{\mathbf{A}}_{\mathrm{zz}}\text{≡(0,xH,0),}$$ where, for example, A_xx stands for the vector potential when H and μ (the proton magnetic moment) are both in the x direction. The three quantities in the bracket are the three Cartesian components of the vector A. It has been found that with this vector potential, a considerable portion of Ramsey's second‐order paramagnetic part can be calculated without considering the excited electronic states of the molecule.