EPR g-tensor Tutorial
Performing the relativistic EPR g-tensor calculations in ReSpect requires the following sequence of steps
SCF(1c) → SCF(4c) → EPR
where the initial SCF(1c) step represents the self-consistent field (SCF) procedure based on a scalar-relativistic, one-component (1c) Hamiltonian and this step is primarily meant to provide a very good guess of initial molecular orbitals for subsequent fully relativistic calculations, where both scalar- and spin-orbit corrections are included variationally. In the second SCF(4c) step, the actual relativistic molecular orbitals are determined by means of SCF with the relativistic four-component (4c) Dirac—Coulomb Hamiltonian. Note that the second-step must be repeated for all three Cartesian directions of non-collinear spin magnetization as required by an approach implemented in ReSpect [1,2]. The final EPR g-tensor is evaluated in the last step, starting from the relativistic molecular orbitals obtained in SCF(4c).
 M. Repisky, S. Komorovsky, E. Malkin, O. L. Malkina, and V. G. Malkin
Relativistic four-component calculations of electronic g-tensors in the matrix Dirac-Kohn-Sham framework
Chem. Phys. Lett. 488, 94-97 (2010)
 S. Gohr, P. Hrobarik, M. Repisky, S. Komorovsky, K. Ruud, and M. Kaupp
Four-component relativistic density functional theory calculations of EPR g- and hyperfine-coupling tensors using hybrid functionals: validation on transition-metal complexes with large tensor anisotropies and higher-order spin-orbit effects
J. Chem. Phys. A 119, 12892-12905 (2015)
To perform the SCF(1c) calculation, execute the command
/path/to/ReSpect/respect --scf --inp=1c --scratch=/path/to/scratch/directory
where arguments mandatory to
starts the SCF procedure;
specifies a name of the input file;
specifies a path to the scratch directory.
A simple example of the input file 1c.inp for a scalar relativistic one-component DFT calculation of GaO with the Douglas–Kroll–Hess Hamiltonian looks like
#1c Kohn-Sham DFT calculation of GaO molecule with DKH2 Hamiltonian scf: geometry: Ga 0.000 0.000 0.000 O 0.000 0.000 1.744 method: ks-dkh2/b3lyp basis: ucc-pvdz charge: 0 multiplicity: 2 maxiterations: 30 nc-model: gauss
Note that a comprehensive list of all SCF keywords can be found here.
Having the initial SCF(1c) step finished, let's move on to the next SCF(4c) step. In order to have the 1c molecular orbitals ready for a restart, we execute the linux command first
ln -sf 1c.50 4c_X.50
which soft-links the ReSpect checkpoint file 1c.50 generated in the previous SCF(1c) calculation to a new checkpoint file 4c_X.50. Now, we can perform the second SCF(4c) step
/path/to/ReSpect/respect --restart --scf --inp=4c_X --scratch=/path/to/scratch/directory
where the additional argument --restart enforces
respect to search for the initial molecular orbitals in the checkpoint file 4c_X.50. An example of the input file 4c_X.inp is
#4c Dirac-Kohn-Sham DFT calculation of GaO molecule with #the Dirac--Coulomb Hamiltonian and the spin magnetization vector along X scf: geometry: Ga 0.000 0.000 0.000 O 0.000 0.000 1.744 spin: X method: mdks/b3lyp basis: ucc-pvdz charge: 0 multiplicity: 2 maxiterations: 30 nc-model: gauss
Here, we replaced the 1c DKH2 Hamiltonian
method:ks-dkh2/dft-functional by the 4c Dirac—Coulomb Hamiltonian
method:mdks/dft-functional. In addition, the keyword
spin: was introduced in order to cover an important aspect associated with EPR g-tensor calculations, namely
it is necessary to perform three indipendent 4c SCF calculations with the spin magnetization vector oriented along three perpendicular Cartesian directions.
The way to accomplish this requirement is to set the keyword
spin:to X direction
or to Y direction
or to Z direction
and rerun the SCF procedure for each direction. Importantly, save the SCF output and checkpoint files with specific suffixes --- _X.out_scf and _X.50 for x-direction, _Y.out_scf and _Y.50 for y-direction, and _Z.out_scf and _Z.50 for z-direction. These name-specific files are required for the final EPR step discussed in the next paragraph.
Having all three SCF(4c) calculations finished successfully, let's perform the final EPR step by running the command
/path/to/ReSpect/respect --gt --inp=epr --start-data="4c_X 4c_Y 4c_Z" --scratch=/path/to/scratch/directory
where the input file for EPR g-tensor calculation epr.inp must contain the block
gt:. A simple example of epr.inp would be
#the EPR g-tensor input block gt: gauge: center-of-mass
A comprehensive list of all EPR g-tensor keywords can be found here.
As a final note, there are several important and worth-to-remember aspects associated with the input syntax, namely
the input is case-insensitive
This means that the program does not distinguish between uppercase and lowercase letters.
the input is insensitive to the number of blank lines and/or comment lines
All comments begin with the number sign (#), can start anywhere on a line and continue until the end of the line.
the input is compliant with the dictionary syntax of the YAML markup language
This means that each input line is represented either by a single
block:statement or by a simple
keyword:valuepair, such as
block1: keyword1: value1 keyword2: value2 ... block2: keyword3: value3 keyword4: value4 ... block3: keyword5: value5 keyword6: value6 ...
It is essential to remember that all members of one
block: are lines beginning at the same indentation level. Whitespace indentation is used to denote the block structure; however, tab characters are never allowed as indentation. The only exception to the YAML-based input syntax is the block
geometry: which utilizes a simple xyz format for the molecular geometry specification.
TIPS & TRICKS
Q: How to scale the speed of light in calculations of g-tensor?
Set the cscale option in the SCF calculation. The scaling value is then automatically transferred to the GT calculation.
Q: Is it possible to scale spin-orbit interaction in calculations of g-tensor?
Yes. To scale SO interaction set soscale option in the SCF calculation. This setting is then automatically transferred to the GT calculation.
Q: Is there a way to launch SCF and EPR calculations without the need to explicitly setup the scratch path by "--scratch=/path/to/scratch/directory"?
Yes, the argument "--scratch=/path/to/scratch/directory" can be saved to the file .respectrc in your home directory. If both the file and the command line argument exist, then ReSpect takes the scratch directory setting from the command line.
Q: How to set the number of processors for parallel SCF and EPR calculations?
For OpenMP parallel calculations, the number of processors can be controlled from the command line by the argument --nt=N, where N ideally refers to the total number of physical cores of a machine. Thus, the command line for launching an OpenMP parallel SCF or EPR job reads
/path/to/ReSpect/respect --nt=N --scf --inp=my-input-file /path/to/ReSpect/respect --nt=N --gt --inp=my-input-file
Note, however, we have assumed here that the scratch path is setup through the file .respectrc (see the previous discussion).
Department of Chemistry
UiT The Arctic University of Norway
Tromsø, NO-9037 Norway