Keywords for Module RICC2

Note that beside the keywords listed below the outcome of the RICC2 program also depends on the settings of most thresholds that influence the integral screening (e.g. $denconv, $scfconv, $scftol) and for the solution of Z vector equation with 4-index integrals (for relaxed properties and gradients) on the settings for integrals storage in semi-direct SCF runs (i.e. $thime, $thize, $scfintunit). For the explanation of these keywords see Section 12.2.5.

$cbas file=auxbasis

Auxiliary basis set for RI approximation. For details Section 12.2.12.

$freeze

Freeze orbitals in the calculation of correlation and excitation energies. For details see Section 12.2.12.

$printlevel 1

Print level. The default value is 1.

$tmpdir /work/thisjob

Specify a directory for large intermediate files (typically three-index coulomb integrals and similar intermediates), which is different from the directory where the RICC2 program is started.

$maxcor 20

The data group $maxcor adjusts the maximum size of core memory in MB which will be allocated during the RI-CC2 run. This keyword can be set in define or with the RIMP2PREP tool, the default is 20MB.
$maxcor has a large influence on computation times for RI-CC2 runs! It is recommended to set $maxcor to ca. 75-85% of the available (physical) core memory.

$spectrum unit

The calculated excitation energies and corresponding oscillator strengths are appended to a file named 'spectrum'. Possible values of unit are eV, nm and cm$^{-1}$ or rcm. If no unit is specified, excitation energies are given in a.u.

$cdspectrum unit

The calculated excitation energies and corresponding rotatory strengths are appended to a file named 'cdspectrum'. unit can have the same values as in $spectrum.

$ricc2

ccs
cis
mp2     energy only
cis(d)  energy only
cis(dinf)
adc(2)
cc2
restart
norestart
hard_restart
nohard_restart
conv    = 8
oconv   = 7
lindep  = 15
maxiter = 25
mxdiis  = 10
maxred  = 100
iprint  = 1
fmtprop = f15.8
geoopt model=cc2 state=(a" 2)
scs  cos=1.2d0   css=0.3333d0
sos
gsonly

specifies the ab initio models (methods) for ground and excited states and the most important parameters and thresholds for the solution of the cluster equations, linear response equations or eigenvalue problems. If more than one model is given, the corresponding calculations are performed successively. Note: The CCS ground state energy is identical with the SCF reference energy, CCS excitation energies are identical to CIS excitation energies. The MP2 results is equivalent to the result from the RIMP2 module. cis(dinf) denotes the iterative CIS(D) variant CIS(D$_\infty$).

mp2 energy only

If the energy only flag is given after the mp2 keyword, it is assumed that only a MP2 ground state energy is requested. This switches on some shortcuts to avoid the computation of intermediates needed e.g. for the calculation of properties, gradients, the $D_1$ diagnostic, etc. or for CIS(D) and CC2 calculations.

cis(d) energy only

If the energy only flag is given after the cis(d) keyword, it is assumed that only excitation energies are requested. This switches on some shortcuts to avoid the computation of intermediates needed e.g. for the generation of improved start vectors for CC2.

(no)restart

If the restart flag is set, the program will try to restart the CC2 calculations from previous solution vectors on file. If the norestart flag is set no restart will be done. Default is to do a restart for CC2 if and only if the file CCR0--1--1---0 exists. Note: There is no restart possibility for CCS/CIS or MP2/CIS(D).

(no)hard_restart

If the hard_restart flag is set, the program will try to reuse integrals and intermediates from a previous calculation. This requires that the restart.cc file has been kept, which contains check sums and some other informations needed. The hard_restart flag is switched on by default, if the restart.cc file is present.

conv

The conv parameter gives the convergence threshold for the CC2 ground state energy as $10^{-\mathrm{conv}}$. The default value is taken from the data group $deneps.

oconv

The oconv parameter gives an additional threshold for the residual of the cluster equations (vector function). If this parameter is given, the iterations for the cluster equations are not stopped before the norm of the residual is $< 10^{-\mathrm{oconv}}$. By default the threshold is set to oconv = conv$-1$, or $10 \times$ deneps if no input for conv is given.

lindep

If the norm of a vector is smaller than $10^{-\mathrm{lindep}}$, the vector is assumed to be zero. This threshold is also used to test if a set of vectors is linear dependent. The default threshold is $10^{-15}$.

maxiter

gives the maximum number of iterations for the solution of the cluster equations, eigenvalue problems or response equations (default: 25).

mxdiis

is the maximum number of vectors used in the DIIS procedures for CC2 ground state or excitation energies (default: 10).

maxred

the maximum dimension of the reduced space in the solution of linear equations (default: 100).

iprint

print level, by default set to 1 or (if given) the the value of the $printlevel data group.

fmtprop

Fortran print format used to print several results (in particular one-electron properties and transition moments) to standard output.

geoopt

specify wavefunction and electronic state for which a geometry optimization is intended. For this model the gradient will be calculated and the energy and gradient will be written onto the data groups $energy and $grad. Required for geometry optimizations using the JOBEX script. Note, that in the present version gradients are only available for ground states at the MP2 and CC2 and for excited states at the CC2 level and not for ROHF based open-shell calculations. Not set by default. The default model is CC2, the default electronic state the ground state. To obtain gradients for the lowest excited state (of those included in the excitation energy calculation, but else of arbitrary multiplicity and symmetry) the short cut s1 can be used. x is treated as synonym for the ground state.

scs

the opposite-spin scaling factor cos and the same-spin scaling factor css can be choosen. If scs is set without further input, the SCS parameters cos=6/5 and css=1/3 are applied. This keyword can presently only be used in connection with MP2.

sos

the SOS parameters cos=1.3 and css=0.0 are applied. This keyword can presently only be used in connection with MP2.

gsonly

the SCS scaling factors are only used for ground state amplitudes (presently unused).

$rir12

r12model
noinv
local
pairenergy

r12model char

char=A or A'
The r12model flag determines which approximation model is used to calculate the RI-MP2-R12 ground state energy.
(Approximation A is used if r12model is absent.)

noinv

Calculates only the orbital-dependent RI-MP2-R12 ground state energy. It reduces the computational cost for the last step of the energy calculation from ${\cal O}(O^4N^2)$ to ${\cal O}(O^2N^2)$ by sacrificing the orbital invariance.
(Default: Both, the orbital-dependent and invariant energies are computed.)

local char

char=boys or pipek
The active occupied molecular orbitals are localized by Boys or Pipek-Mezey method. Currently, the local flag is restricted to closed shell cases within approximation A.

pairenergy

In addition to the RI-MP2-R12 summary, the R12-pair energies are printed out.

$excitations

irrep=au  multiplicity=1 nexc=4  npre=6  nstart=8
irrep=bg  multiplicity=3 nexc=2  npre=4  nstart=5
spectrum states=all operators=diplen,dipvel
exprop   states=all operators=qudlen
xgrad    states=(ag{3} 1)
conv    = 6
thrdiis = 2
preopt  = 3
leftopt
bothsides

In this data group you have to give additional input for calculations on excited states:

irrep

the irreducible representation.

multiplicity

spin multiplicity (1 for singlet, 3 for triplet); default: singlet, not needed for UHF.

nexc

the number of excited states to be calculated within this irrep and for this multiplicity.

npre

the number of roots used in preoptimization steps (default: npre $=$ nexc).

nstart

the number of start vectors generated or read from file (default: nstart $=$ npre).

spectrum

This flag switches on the calculation of oscillator strengths for excited state--ground state transitions. Setting the parameter states=all is mandatory for the calculation of transition properties in the present version. The operators flag can be followed by a list of operators (see below) for which the transition properties will be calculated. Default is to compute the oscillator strengths for all components of the dipole operator.

exprop

require calculation of first-order properties for excited states. For the states option see spectrum option above; for details for the operators input see below.

xgrad

request calculation of the gradient for the total energy of an excited state. If no state is specified, the gradient will be calculated for the lowest excited state included in the calculation of excitation energies (Note that only a single state should be specified; simultaneous calculation of gradients for several states is in the present version not possible.).

conv

convergence threshold for norm of residual vectors in eigenvalue problems is set to $10^{-\tt conv}$. If not given, a default value is used, which is chosen as $\max(10^{-\tt conv},10^{-\tt oconv},10^{-6})$,
where conv refers to the values given in the data group $ricc2.

preopt

convergence threshold used for preoptimization of CC2 eigenvectors is set to $10^{-\tt preopt}$ (default: 3).

thrdiis

threshold ( $10^{-\tt thrdiis}$) for residual norm below which DIIS extrapolation is switched on in the modified Davidson algorithm for the non-linear CC2 eigenvalue problem (default: 2).

leftopt

If the flag leftopt is set the left eigenvectors are computed (default is to compute the right eigenvectors, for test purposes only).

bothsides

The bothsides flag enforces the calculation of both, the left and the right eigenvectors (for test purposes only).

$response

fop unrelaxed_only operators=diplen
gradient
conv = 6
zconv = 6
semicano
nosemicano
thrsemi = 3

In this data group you have to give additional input for the calculation of ground state properties and the solution of response equations:

fop

This flag switches on the calculation of ground state first-order properties (expectation values). The operators flag can be followed by a list of operators (see below) for which the first-order properties will be calculated. Default is to compute the components of the dipole and the quadrupole moment. The option unrelaxed_only suppress the calculation of orbital-relaxed first-order properties, which require solution the CPHF-like Z-vector equations. Default is the calculation of unrelaxed and orbital-relaxed first-order properties. The unrelaxed_only option will be ignored, if the calculation of gradients is requested (see gradient option below and geoopt in data group $ricc2).

gradient

require calculation of geometric gradients. In difference to the geoopt keyword in the data group $ricc2 this can be used to compute gradients for several methods within a loop over models; but gradients and energies will not be written to the data groups $grad and $energy as needed for geometry optimizations. Note, that in the present version gradients are only available for MP2 and CC2 and only for a closed-shell RHF reference.

conv

convergence threshold for norm of residual vectors in linear response equations is set to $10^{-\tt conv}$. If not given in the $response data group, a default value is used, which is chosen as $\max(10^{-\tt conv},$
$10^{-\tt oconv},10^{-6})$, where conv and oconv refer to the values given in the data group $ricc2.

zconv

convergence threshold for the norm of the residual vector in the solution of the Z vector equations will be set to $10^{-\tt zconv}$.

semicano

use semi-canonical formulation for the calculation of (transition) one-electron densities. Switched on by default. The semi-canonical formulation is usually computationally more efficient than the non-canonical formulation. Exceptions are systems with many nearly degenerate pairs of occupied orbitals, which have to be treated in a non-canonical way anyway. (See also explanation for thrsemi below).

nosemicano

use non-canonical formulation for the calculation of (transition) one-electron densities. Default is to use the semi-canonical formulation.

thrsemi

the threshold for the selection of nearly degenerate pairs of occupied orbitals which (if contributing to the density) have to be treated in a non-canonical fashion will be set to $10^{-\tt thrsemi}$. If set to tight the semi-canonical algorithm will become inefficient, if the threshold is to large the algorithm will become numerical unstable

Common options for keywords in the data groups $ricc2, $response, and $excitations:

operators=diplen,dipvel

input of operator labels for first-order properties, transition moments, etc. Currently implemented operators/labels are

overlap

overlap (charge) operator: the integrals evaluated in the AO basis are $\langle\mu\vert\nu\rangle$

diplen

dipole operator in length gauge: $\langle\mu\vert r_i^O\vert\nu\rangle$ with $i$ = $x$, $y$, $z$; the index $O$ indicates dependency on the origin (for expectation values of charged molecules), which in the present version is fixed to $(0,0,0)$
(all three components, individual components can be specified with the labels xdiplen, ydiplen, zdiplen).

dipvel

dipole operator in velocity gauge: $\langle\mu\vert\nabla_i\vert\nu\rangle$
(all three components, individual components can be specified with the labels xdipvel, ydipvel, zdipvel).

qudlen

quadrupole operator $\langle\mu\vert r^O_i r^O_j\vert\nu\rangle$
(all six components, individual components can be specified with the labels xxqudlen, xyqudlen, xzqudlen, yyqudlen, yzqudlen, zzqudlen).
If all six components are present, the program will automatically give the electronic second moment tensor (which involves only the electronic contributions) $M_{ij}$, the isotropic second moment $\alpha = \frac{1}{3}$   tr$M$ and the anisotropy

$$\beta = \sqrt{\frac{1}{2}<tex2html_comment_mark>1674 \sum_{i=x}^z (M_{ii}-M_{i+1,i+1})^2 +3\sum_{i=x}^z M_{i,i+1}^2 } .$$

Furthermore the traceless quadrupole moment

$$\Theta_{ij} = \frac{1}{2}\langle 3 r_ir_j -r^2\delta_{ij}\rangle$$

(including nuclear contributions) is given.

angmom

angular momentum $\langle\mu\vert L^O_i\vert\nu\rangle$
(all three components, individual components can be specified with the labels xangmom, yangmom, zangmom).

nef

electronic force on nuclei $\langle\mu\vert\frac{Z_I r_i^I}{{r^I}^3}\vert\nu\rangle$, where $Z_I$ is the charge of the nucleus $I$ and $r^I$ is the position vector of the electron relative to the nucleus (all three components for all nuclei: the labels are xnef001, ynef001, znef001, xnef002, etc. where the number depends on the order in the coord file).

states=all

specification of states for which transition moments or first-order properties are to be calculated. The default is all, i.e. the calculations will be done for all excited states for which excitation energies have been calculated. Alternatively, one can select a subset of these listed in parentheses, e.g. states=(ag{3} 1,3-5; b1u{1} 1-3; b2u4). This will select the triplet $a_g$ states no. 1, 3, 4, 5 and the singlet $b_{1u}$ states no. 1, 2, 3 and the singlet (which is default if no {} is found) $b_{2u}$ state no. 4.

$cgrad 1000

Calculate the error functional $\delta_{\mathrm{RI}}$ for the RI approximation of $(ai\vert bj)$ integrals

$$\delta_{\mathrm{RI}} = \frac{1}{4} \frac{\vert\langle ab \vert\v... ..._{\mathrm{RI}} \vert^2 }{ \epsilon_a - \epsilon_i + \epsilon_b - \epsilon_j }$$

and its gradients with respect to exponents and coefficients of the auxiliary basis set as specified in the data group $cbas. The results are written to $egrad scaled by the factor given with the keyword $cgrad and can be used to optimize auxiliary basis sets for RI-MP2 and RI-CC2 calculations (see Section 1.5).