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RelEPro (renamed from RelED) is a utility program to calculate one-electron properties based on the eXact 2-Component (X2C) all-electron quasi-relativistic Hamiltonian and its local approximations.
Version 1.2.1 (June 04, 2024).
Version 1.2.0 (May 14, 2024).
Hamiltonians:
Properties:
The finite nuclear charge distribution must be used in the quantum chemistry calculations. See the following Table for the supported quantum chemistry programs.
It is necessary to modify the basis functions of the interested heavy atom to obtain reliable results. For CD and ED, the s-functions should be decontracted and supplemented with 2 to 4 additional very steep primitive s-functions. Optionally, do the same things for p-functions. For EFG, the p-functions should be decontracted and supplemented with 2 to 4 very steep primitive p-functions. Do the same things for d- or f-functions if there are also d or f valence orbitals.
According to the linear response approach, the general formula of a first-order one-electron property can be represented as
∂E/∂μ = tr(PQR ∂HX2C/∂μ)
where PQR is the quasi-relativistic (QR) density matrix constructed using occupied molecular orbitals (MOs) and ∂HX2C/∂μ is the first-order derivative of the X2C Hamiltonian with respect to an external perturbation μ depending on the property to be calculated.
The quasi-relativistic canonical, pseudo-canonical, or natural MOs may be calculated at the X2C (= Dirac-exact NESC), BSS (= IODKH = IOTC), or DKHn (scalar-)relativistic level of theory (e.g. X2C/DFT, DKH2/CCSD, and so on) using a third-party quantum chemistry program (see the following table), and saved in a MOLDEN or FCHK data file. However, the MOLDEN file is not strictly defined, and therefore it has to be converted to an "official" form with the help of Molden2AIM or Multiwfn.
TABLE 1. Quasi-relativistic Hamiltonians with the finite nuclear model implemented in different quantum chemistry programs
Program | Version | QR in PQR | Data format |
---|---|---|---|
BAGEL | sf-DKH2 | MOLDEN | |
BDF | ≥ 2018 | sf-X2C | MOLDEN |
CFour | ≥ 2.1 | sf-X2C | MOLDEN |
Cologne | ≥ 2010 | sf-X2C | FCHK |
X2C | FCHK | ||
Columbus | sf-X2C, sf-BSS, sf-DKHn | MOLDEN; through (Open)Molcas | |
Dalton | ≥ 2015 | sf-DKH2 | MOLDEN |
Gaussian | ≥ 09 | sf-DKH2, sf-DKH4 | FCHK |
DKH4 | FCHK | ||
(Open)Molcas | sf-X2C, sf-BSS, sf-DKHn | MOLDEN | |
Molpro | ≥ 2019 | sf-X2C, sf-DKHn | MOLDEN |
MRCC | sf-X2C | MOLDEN; through CFour | |
NWChem | ≥ 7.0 | sf-DKH2, sf-DKH3, sf-X2C | MOLDEN |
ORCA | ≥ 6.0 | sf-DKH2, sf-X2C | MOLDEN |
PySCF | sf-X2C | MOLDEN | |
Turbomole | ≥ 7.3 | sf-X2C, sf-BSS, sf-DKHn | MOLDEN |
Some other quantum chemistry programs with quasi-relativistic Hamiltonians do not support the finite nuclear model or cannot save MOLDEN/FCHK files, and therefore are not listed here.
RelEPro can calculate the one-electron integrals in ∂HX2C/∂μ and combine them together with PQR to get the one-electron property ∂E/∂μ. For theoretical details, please refer to our papers.
The local X2C Hamiltonians have been defiend in the following papers. If there is no HA-HA bond in a molecule (HA: 5d or heavier atoms), the most efficient approximations DLU and AU are usually accurate enough.
Run make
in the RelEPro/source directory, where gfortran
is used by default. In Makefile you may also specify other Fortran 90 compilers like nvf90
(pgf90
). If the compilation is successful you will see the binary program in RelEPro/bin .
For ifort
+ mkl
, run make -f Makefile-mkl
instead.
(Ignore this step for FCHK files.) Save a new MOLDEN file using Molden2AIM or Multiwfn.
Edit the input file job.inp
(see below for the descriptions) and the batch script run1.bat
(Windows) or run1.sh
(Linux/MacOS) in RelEPro/work as needed.
(a) Windows. Double-click run1.bat
and check the results in job.out
.
(b) Linux/MacOS. Run the following commands in the terminal and
check the results in job.out
.
chmod +x run1.sh
./run1.sh
The available keywords and options are grouped by namelists.
$Contrl
groupThe keywords and their default options are
$contrl
prop=' ' iham=0 minz=0 popu=0
$end
The options of prop
are +dip
, +cd
, +ed
, and +efg
,
which perform DIP, CD, ED, and EFG calculations, respectively.
These options may also be combined together. For example, prop='+efg+ed'
will calculate both EFG and ED.
iham
specifies the Hamiltonian. Its options are 0 (=4), 1 (non-relativistic), 2 (X2C), 3 (X2C-DLXR), 4 (X2C-AXR), 5 (X2C-DLU), 6 (X2C-AU).
minz
specifies the atoms to calculate CD, ED, or EFG. Ir can be 0 (all the atoms), < 0 (heavy atoms with Z = |minz|), or > 0 (heavy atoms with Z ≥ minz).
popu = 1
does population analysis for ED and EFG. For EFG, however, population analysis of spinor orbitals has not been implemented yet.
$QCData
groupThere is only one keyword fnam
to specify the name of the MOLDEN/FCHK data file. For example,
$qcdata
fnam="fef6.molden"
$end
$PChar
group (optional for DIP and EFG)External point charges needed in the DIP and EFG calculations are not included in the MOLDEN/FCHK data file.
They have to be provided after the $PChar
group explicitly.
The unit of Cartesian coordinates can be Bohr (unit=0
; default) or Angstrom (unit=1
).
$pchar unit=0 $end
Q1 x1 y1 z1
Q2 x2 y2 z2
...
$NQMDat
group (optional for EFG)In the NQCC and Mössbauer NQS calculations, the nuclear quadrupole moment (NQM) parameters of common nuclides are taken from Ref.8.
The NQM parameters of the other nuclides may be found in Refs.9-11 and provided after the $NQMDat
group (in millibarn).
$nqmdat $end
i_Atom NQM_value_i
j_Atom NQM_value_j
...
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