## EPR A-tensor Tutorial

Performing the relativistic calculation of EPR hyperfine coupling constant (A-tensor) 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 A-tensor is evaluated in the last step, starting from the relativistic molecular orbitals obtained in SCF(4c).

[1] E. Malkin, M. Repisky, S. Komorovsky, P. Mach, O. L. Malkina, and V. G. Malkin
Effects of finite size nuclei in relativistic four-component calculations of hyperfine structure
J. Phys. Chem. 134, 044111 (2011)

[2] 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 respect mean

• --scf
starts the SCF procedure;

• --inp
specifies a name of the input file;

• --scratch
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 A-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

• spin: X

or to Y direction

spin: Y

or to Z direction

spin: Z

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 --hfcc --inp=epr --start-data="4c_X 4c_Y 4c_Z" --scratch=/path/to/scratch/directory

where the input file for EPR A-tensor calculation epr.inp must contain the block hfcc:. A simple example of epr.inp would be

#the EPR A-tensor input block
hfcc:
nmm-model: point
isotope:
Ga: 69
O:  17


A comprehensive list of all EPR A-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:value pair, 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 A-tensor?

Set the cscale option in the SCF calculation. The scaling value is then automatically transferred to the HFCC calculation.

Q: Is it possible to scale spin-orbit interaction in calculations of A-tensor?

Yes. To scale SO interaction set soscale option in the SCF calculation. This setting is then automatically transferred to the HFCC 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 --hfcc --inp=my-input-file


Note, however, we have assumed here that the scratch path is setup through the file .respectrc (see the previous discussion).

August 31, 2020

February, 2019

August 31, 2020

May 11, 2020