Units for NMR Shift

[Ronald Cohen]

I am struggling with the lack of documentation for the NMR calculations. What are the units in the SHIFT files? I find:

! Conversion factors

      ! factor for the CHEMICAL SHIFTS: alpha^2 *  ppm.

      nmr_env%shift_factor = (1.0_dp/137.03602_dp)**2*1.0E+6_dp/cell%deth

      ! factor for the CHEMICAL SHIFTS: alpha^2 *  ppm.

      nmr_env%shift_factor_gapw = (1.0_dp/137.03602_dp)**2*1.0E+6_dp

      ! chi_factor =  1/4 * e^2/m * a_0 ^2

      nmr_env%chi_factor = 1.9727566E-29_dp/1.0E-30_dp ! -> displayed in 10^-30 J/T^2

      ! Factor to convert 10^-30 J/T^2 into ppm cgs = ppm cm^3/mol

      ! = 10^-30 * mu_0/4pi * N_A * 10^6 * 10^6  [one 10^6 for ppm, one for m^3 -> cm^3]

      nmr_env%chi_SI2ppmcgs = 6.022045_dp/1.0E+2_dp

      ! Chi to Shift: 10^-30  *  2/3  mu_0 / Omega  * 1/ppm

      nmr_env%chi_SI2shiftppm = 1.0E-30_dp*8.37758041E-7_dp/ &

                                (cp_unit_from_cp2k(cell%deth, "angstrom^3")*1.0E-30_dp)*1.0E+6_dp

      IF (output_unit > 0) THEN

         WRITE (output_unit, "(T2,A,T65,ES15.6)") "NMR| Shift gapw radius (a.u.) ", nmr_env%shift_gapw_radius

         IF (nmr_env%do_nics) THEN

            WRITE (output_unit, "(T2,A,T50,I5,A)") "NMR| NICS computed in ", nmr_env%n_nics, " additional points"

            WRITE (output_unit, "(T2,A,T60,A)") "NMR| NICS coordinates read on file ", TRIM(nics_file_name)

         END IF

         WRITE (output_unit, "(T2,A,T65,ES15.6)") "NMR| Shift factor (ppm)", nmr_env%shift_factor

         IF (gapw) THEN

            WRITE (output_unit, "(T2,A,T65,ES15.6)") "NMR| Shift factor gapw (ppm)", nmr_env%shift_factor_gapw

         END IF

         WRITE (output_unit, "(T2,A,T65,ES15.6)") "NMR| Chi factor (SI)", nmr_env%chi_factor

         WRITE (output_unit, "(T2,A,T65,ES15.6)") "NMR| Conversion Chi (ppm/cgs)", nmr_env%chi_SI2ppmcgs

         WRITE (output_unit, "(T2,A,T65,ES15.6)") "NMR| Conversion Chi to Shift", nmr_env%chi_SI2shiftppm

      END IF

And in the output of that run:

        Inizialization of the NMR environment

 NMR| Shift gapw radius (a.u.)                                     1.133836E+02

 NMR| Shift factor (ppm)                                           6.533065E-03

 NMR| Shift factor gapw (ppm)                                      5.325134E+01

 NMR| Chi factor (SI)                                              1.972757E+01

 NMR| Conversion Chi (ppm/cgs)                                     6.022045E-02

 NMR| Conversion Chi to Shift                                      6.935882E-04

So to convert the numbers in the SHIFT files is the correct conversion is 6.022045E-02 or 6.935882E-04? 

Thank you!

Sincerely,

Ron Cohen