Parity-violation contribution to nuclear spin-rotation constants
Introduction
In this tutorial we introduce the calculation of parity violation contribution to nuclear spin-rotation tensors as given in the DIRAC code.
The parity-violation contribution to nuclear spin-rotation (PVCNSR) tensor of a nucleus \(N\) is given by
where \(\rho_N({\bf r})\) is the normalized nuclear charge density; \({\bf I}\) is the inertia tensor of the molecule and \({\bf J}_e = \left({\bf r} - {\bf R}_{CM} \right) \times {\bf p}+{\bf S}_e\) is the electronic total angular momentum.
Application to the H2O2 molecule
As an example, we show a calculation of the PV contribution to the NSR constant of the oxygen nucleus at the Hydrogen peroxide molecule. The input file pvcsr.inp is given by
**DIRAC
.TITLE
Parity-violation contribution to spin-rotation
.WAVE FUNCTION
.PROPERTIES
**HAMILTONIAN
.URKBAL
**INTEGRALS
.SELECT
1
3
*READIN
.UNCONTRACT
**WAVE FUNCTIONS
.SCF
*SCF
.EVCCNV
1.0E-7
**PROPERTIES
.PVCSR
.PRINT
2
*LINEAR RESPONSE
.THRESH
1.0D-7
*END OF
whereas the molecular input file H2O2.mol is
INTGRL
H2O2 molecule
cc-pVDZ basis
C 2 0
1. 2
H1 -0.690815 -1.726149 1.667775
H2 0.690815 1.726149 1.667775
LARGE BASIS cc-pVDZ
8. 2
O3 0.000000 -1.407846 0.000000
O4 0.000000 1.407846 0.000000
LARGE BASIS cc-pVDZ
FINISH
The calculation is run using:
pam --inp=pvcsr --mol=H2O2
As a result, PVCNSR are obtained at the coupled Hartree-Fock level. The code also works at the DFT level.
Reading the output file
As the PROPERTIES_.PRINT flag in the input file is set to 1, the results are fully detailed and given in Hz.
The PVCNSR of the oxygen nucleus will look like:
Parity-violation contribution to nuclear spin-rotation constant (Hz) for the zero-value g-factor nucleus O3
-----------------------------------------------------------------------------------------------------------
WARNING: Nuclear g-value NOT available for isotope of mass 15.995
Total PVC to nuclear spin-rotation constant
-------------------------------------------
A -0.17995229E-05 0.38632077E-05 0.55199909E-05
B -0.58143612E-04 0.16007781E-05 -0.10392856E-03
C -0.11600712E-03 0.11286829E-03 -0.17978966E-05
iso -0.66554712E-06
M^LR-L(e-e)
-----------
A -0.18709065E-05 0.38692922E-05 0.55349517E-05
B -0.58168472E-04 0.15874564E-05 -0.10396608E-03
C -0.11602249E-03 0.11290509E-03 -0.17906721E-05
iso -0.69137409E-06
M^LR-S(e-e)
-----------
A 0.71236835E-07 -0.52291482E-08 -0.13478821E-07
B 0.13889115E-07 0.13475745E-07 0.14222802E-07
C -0.65750397E-08 -0.11806627E-07 -0.73909112E-08
iso 0.25773890E-07
M^LR-L(e-p)
-----------
A 0.14586154E-09 -0.88205576E-09 -0.15419970E-08
B 0.11276044E-07 -0.15416722E-09 0.23348137E-07
C 0.22681711E-07 -0.25045439E-07 0.16651050E-09
iso 0.52734939E-10
M^LR-S(e-p)
-----------
A 0.96137869E-12 0.26634709E-10 0.60015457E-10
B -0.30494980E-09 0.15492645E-12 -0.54368827E-10
C -0.73067273E-09 0.57770647E-10 -0.81830548E-13
iso 0.34482486E-12
As it can be seen, the total SR constant of the oxygen nucleus is given. The linear response function is further separated in their (e-e) and (e-p) parts, as well as in their \(\mathbf{L}\) and \(\mathbf{S}\) parts.