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 15.2.5.

$cbas file=auxbasis

Auxiliary basis set for RI approximation. For details Section 15.2.12.

$freeze

Freeze orbitals in the calculation of correlation and excitation energies. For details see Section 15.2.12.

$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.

$laplace

conv = 5

The purpose of this data group is twofold: It activates the Laplace-transformed implementation of SOS-MP2 in the ricc2 module (if the sos option has been specified in $ricc2) and it provides the options to specify the technical details for the numerical Laplace-transformation.

conv

Threshold for the numerical integration used for the Laplace transformation of orbital energy denominators. The grid points for the numerical integration are determined such that is the remaining root mean squared error (RMSE) of the Laplace transformation is < 10^-conv. By default the threshold is set to the value of conv given in $ricc2 (see below).

$ricc2

ccs
cis
mp2     d1diag
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
d1diag

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_∞).

mp2 d1diag

Request the calculation of the D₁ diagnostic in MP2 energy calculations (ignored in MP2 gradient calculations). Note that the evaluation of the D₁ diagnostic increases the computational costs of the RI-MP2 energy calculation roughly by a factor of 3.

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^-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^-oconv. By default the threshold is set to oconv = conv-1, or 10× deneps if no input for conv is given.

lindep

If the norm of a vector is smaller than 10^-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.

d1diag

request the calculation of the D₁ diagnostic for the ground state wavefunction. Only needed for MP2 (see above for the alternative input option mp2 d1diag). For all other correlated methods the D₁ diagnostic is evaluated by default (without significant extra costs).

$rir12

ansatz    
r12model  
comaprox  
cabs      
examp     
pairenergy
local     
corrfac   
cabsingles
ump2fixed

ansatz char

char=1, 2* or 2
The ansatz flag determines which ansatz is used to calculate the RI-MP2-F12 ground state energy.
(Ansatz 2 is used if ansatz is absent.)

r12model char

char=A, A' or B
The r12model flag determines which approximation model is used to calculate the RI-MP2-F12 ground state energy.
(Ansatz B is used if r12model is absent.)

comaprox char

char=F+K or T+V
The comaprox flag determines the method used to approximate the commutator integrals [T, f₁₂].
(Approximation T+V is used if comaprox is absent.)

cabs char val

char=svd or cho
The cabs flag determines the method used to orthogonalize the orbials of the CABS basis. val is the threshold below which CABS orbitals are removed from the calculation.
(svd 1.0d-08 is used if cabs is absent.)

examp char

char=noinv, fixed or inv
The examp flag determines which methods are used to determine the F12 amplitudes. For inv the amplitudes are optimised using the orbital-invariant method. For fixed and noinv only the diagonal amplitudes are non-zero and are either predetermined using the coalescence conditions (fixed), or optimised (noinv--not orbital invariant). If char=inv, the F12 energy contribution is computed using all three methods.
(The fixed method is used if examp is absent.)

pairenergy char

char=off or on
If char=off (default), the print out of the F12 contribution to the pair energies is supressed. The summary of the RI-MP2-F12 correlation energies is always printed out.

local char

char=off, 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 and the linear correlation factor. If local is absent, no localization is performed.

corrfac char

char=LCG or R12
The corrfac flag determines which correlation factor is used for the geminal basis. LCG requires the data group $lcg, which contains the information regarding exponents and coefficients of the linear combination of Gaussians.

cabsingles char

char=off or on
The cabsingles flag determines whether or not the single excitations into the CABS basis are computed.
The CABS singles are computed in any case if the CABS Fock matrix elements are computed anyway for the F12 calculation (i.e., for ansatz 2 or r12model B or comaprox F+K).

ump2fixed char

char=diag or full
The umpfixed flag controls which fixed-amplitude method is used for calculations using ROHF or UHF references. full is more computationally demanding than diag, but gives energies closer to the inv method. If ump2fixed is absent, the full method is used.

$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

zpreopt

threshold for preoptimizating the so-called Z vector (i.e. the lagrangian multipliers for orbital coefficients) with a preceding RI-CPHF calculation with the cbas auxiliary basis. The RI-CPHF equations will be converged to a residual error < 10^{-$\tt zpreopt$}. Default is zpreopt=4. This preoptimization can reduce significantly the computational costs for the solution of the Z vector equations for large basis sets, in particular if they contain diffuse basis functions. For calculations on large molecules with small or medium sized basis sets the preoptimization becomes inefficient compared to the large effects of integral screening for the conventional CPHF equations and should be disabled. This option is automatically disabled for ricc2 calculations based on foregoing RI-JK Hatree-Fock calculation.

nozpreopt

disable the preoptimization of the Z vector by a preceding RI-CPHF calculation with the cbas basis set. (Note that the preoptimization is automatically deactivated if the ricc2 calculation is based on a foregoing RI-JK Hatree-Fock calculation.)

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 〈μ| ν〉

diplen

dipole operator in length gauge: 〈μ| r_i^O| ν〉 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: 〈μ|∇_i| ν〉
(all three components, individual components can be specified with the labels xdipvel, ydipvel, zdipvel).

qudlen

quadrupole operator 〈μ| r^O_ir^O_j| ν〉
(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 α = ${\frac{{1}}{{3}}}$trM and the anisotropy

$$\sqrt{{\frac{1}{2}<tex2html_comment_mark>1880 \sum_{i=x}^z (M_{ii}-M_{i+1,i+1})^2 +3\sum_{i=x}^z M_{i,i+1}^2 }}$$

Furthermore the traceless quadrupole moment

$${\frac{{1}}{{2}}}$$

(including nuclear contributions) is given.

angmom

angular momentum 〈μ| L^O_i| ν〉
(all three components, individual components can be specified with the labels xangmom, yangmom, zangmom).

nef

electronic force on nuclei 〈μ|${\frac{{Z_I r_i^I}}{{{r^I}^3}}}$| ν〉, 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.

$D2-diagnostic

Calculate the double-substitution-based diagnostics D₂.

$cc2_natocc

Write MP2/CC2 natural occupation numbers and natural orbitals to a file.

$cgrad 1000

Calculate the error functional δ_RI for the RI approximation of (ai| bj) integrals

δ_RI = $${\frac{{1}}{{4}}}$$$${\frac{{\vert\langle ab \vert\vert ij \rangle_{exact} - \langle a... ...athrm{RI}} \vert^2 }}{{ \epsilon_a - \epsilon_i + \epsilon_b - \epsilon_j }}}$$

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).