25.2.23 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 25.2.10.

$cbas file=auxbasis

Auxiliary basis set for RI approximation.

$freeze

Freeze orbitals in the calculation of correlation and excitation energies. For details see Section 25.2.4.

$core_excitations

Molecular orbitals out which core excitations are allowed. The syntax for this data group is the same as for $freeze.

$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 n unit reference

The data group $maxcor adjusts the maximum size of core memory which will be allocated during the ricc2 calculation. $maxcor has a large influence on computation times. It is recommended to set $maxcor to ca. 75–85% of the available physical core memory. For further details see subsection 25.2.3.

$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 $< 10^{-\mathrm{conv}}$. 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(di)
adc(2)
cc2
restart on/off
hard_restart on/off
conv    = 8
oconv   = 7
lindep  = 14
maxiter = 25
mxdiis  = 10
maxred  = 100
shift   = 0.d0
iprint  = 1
fmtprop = f15.8
geoopt model=cc2 state=(a" 2)
scs  cos=1.2d0   css=0.3333d0
sos

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(di) denotes the iterative CIS(D) variant CIS(D$_\infty$).

mp2 d1diag: Request the calculation of the $D_1$ diagnostic in MP2 energy calculations (ignored in MP2 gradient calculations). Note that the evaluation of the $D_1$ 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.
restart on/off: If the restart flag is not disabled, the program will try to restart from previous solution vectors on file if it finds any. If the restart flag is set to off no restart from previous solution vectors will be done. The flag is by default set to on.
hard_restart on/off: 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 information needed. The hard_restart flag is switched on by default, if the restart.cc file is present and no geometry optimization is done (i.e. the option geoopt is not set).
conv: The conv parameter gives the convergence threshold for the ground state energy for the iterative coupled-cluster methods 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 $10^{-14}$.
maxiter: gives the maximum number of iterations for the solution of the cluster equations, eigenvalue problems or response equations (per default set to 25, or if found in the control file, to the value of $scfiterlimit).
mxdiis: is the maximum number of vectors used in the DIIS procedures for 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 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 chosen. 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.

$rir12

ansatz    
r12model  
comaprox  
cabs      
examp     
r12orb
pairenergy
corrfac   
cabsingles
f12metric

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 $[T,f_{12}]$.
(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 orbitals 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 with flip or noflip
The examp flag determines which methods are used to determine the F12 amplitudes. For inv the amplitudes are optimized 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 optimized (noinv—not orbital invariant). If char=inv, the F12 energy contribution is computed using all three methods. For open-shell calculations noflip supresses the use of spin-flipped geminal functions.
(The fixed flip method is used if examp is absent.)
pairenergy char: char=off or on
If char=off (default), the print out of the standard and F12 contributions to the pair energies is suppressed. The summary of the RI-MP2-F12 correlation energies is always printed out.
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 or *
The cabsingles flag determines whether or not the single excitations into the CABS basis are computed. Neglect of the EBC (virtual-CABS) Fock matrix elements is activated by .
The default is to always compute the CABS singles correction if the CABS Fock matrix elements are anyway available as a byproduct of the F12 calculation (i.e., for ansatz 2 or r12model B or comaprox F+K).
r12orb char: char=hf, rohf, boys pipek or arb
The r12orb flag controls which orbitals are used for the F12 geminal basis functions. With hf the (semi)-canonical Hartree–Fock orbitals are used (default). For ROHF-based UMP2 calculations rohf orbitals can be used, which also implies that the $freeze data group options refer to ROHF rather than semi-canonical orbitals. For closed-shell species, localised orbitals can be used with either the Boys or Pipek-Mezey method. For the non-(semi)-canonical options, the r12orb noinv F12 energy correction is evaluated using active occupied orbitals transformed to the same basis as the orbitals in the geminal function. The option arb uses the semi-canonicalised reference orbitals for the F12 correction, but makes no assumption about whether or not these orbitals are converged HF orbitals and is appropriate for computing F12 corrections using e.g. DFT or Brueckner orbitals (Note, that the data group $non-canonical MOs should be set in this case).
no_f12metric
f12metric: If no_f12metric is selected the coulomb metric is used in the density fitting scheme to calculate the four index integrals over the operators $f_{12}$, $f_{12}g_{12}$, $f_{12}^{2}$ and $f_{12}r_{12}$. If f12metric is selected the operator’s own metric is used. The default for the ricc2 program is no_f12metric, while the pnoccsd program can only be used with f12metric, where it is therefore the default.

$excitations

irrep=au  multiplicity=1 nexc=4  npre=6  nstart=8 ncore=1
irrep=bg  multiplicity=3 nexc=2  npre=4  nstart=5
spectrum states=all operators=diplen,dipvel
tmexc    istates=all fstates=all operators=diplen,dipvel
exprop   states=all operators=qudlen
twophoton states=all operators=(diplen,diplen) freq=0.1d0
momdrv   states=all operators(diplen,soc) freq=0.0d0
xgrad    states=(ag{3} 1)
conv    = 6
thrdiis = 2
thrpreopt = 3
firstside right
bothsides off
oldnorm   off
maxiter = 25
mxdiis  = 10
maxred  = 100
iprint  = 1

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

irrep

the irreducible representation with the additional suboptions:

multiplicity: spin multiplicity (1 for singlet, 3 for triplet); default: singlet, not used for UHF.
nexc: the number of excited states to be calculated within this irrep and for this multiplicity (mandatory suboption).
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).
ncore: the number of core holes for the excited states requested in this input line, possible values are 0 and 1, default: 0.

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.

tmexc

This flag switches on the calculation of oscillator strengths for excited state—excited state transitions. Specifying the initial and final states via istates=all and fstates=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.

twophoton

request the calculation of two-photon transition moments between ground and excited states. It recognizes the optional suboptions states for specifying the states for which the two-photon transition moments should be computed, operators for specifying a list of pairs of one-electron transition operators, and freq for a list of frequencies for one of the photons. If these suboptions are specified, two-photon transition moments are computed per default for all requested singlet states, dipole operators (in the length representation) and photon energies which are equal 1/2 of the transition energies.

momdrv

request the calculation of derivatives of transition moments between ground and excited states. It recognizes the optional suboptions states for specifying the states for which the two-photon transition moments should be computed, operators for specifying a list of pairs of one-electron transition operators. For phosphorescence lifetimes operators should be set to (diplen,soc) and freq to 0.0d0.

exprop

requests the 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. The simultaneous calculation of gradients for several state is 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.

thrpreopt

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).

firstside right

With this option one can select whether the right or left eigenvalue problem is solved for excitation energies, or solve first, if both eigenvectors are needed. It can be set to right (default) or left (for test purposes only).

bothsides

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

oldnrom

The oldnorm flag (on,off) switches the program to the old normalization of the eigenvectors and $\%T_1$ and $\%T_2$ diagnostics which were identical with those used in the CC response code of the Dalton program.

maxiter, mxdiis, maxred, iprint

Overwrites the values set in $ricc2 in the routines for the calculations of excitation energies and eigenvectors.

roothome

Declares that the requested excitations are specified with their target vectors in the $roothome section.

$response

fop unrelaxed operators=diplen
sop operators=(diplen,diplen) freq=0.077d0,0.089d0
top operators=(diplen,diplen,angmom) freq=0.077d0,-0.077d0
cpp=off gamma=4.5563d-3
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 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 option will be ignored, if the calculation of gradients is requested (see gradient option below and geoopt in data group $ricc2).
sop: requests the calculation of ground state second-order properties as e.g. dipole polarizabilities. The operators flag has to be followed by a comma seperated pair of operators. (If more pairs are needed they have to be given with additional sop commands.) Default is to compute all symmetry-allowed elements of the dipole-dipole polarizability. With the freq flag one can specify a list of frequencies (default is to compute static polarizabilities). The relaxed flag switched from the unrelaxed approach, which is used by default, to the orbital-relaxed approach. Note that the orbital-relaxed approach can only be used in the static limit (freq=0.0d0). For further restrictions for the computation of second-order properties check Chapter 10.5. In combination with damped response (CPP), the flag abscpp can be used to request the operator combinations needed to compute absorption spectra within the length gauge of the dipole operator, and ecdcpp to request the operator combinations for ECD spectra within the velocity gauge of the dipole operator. Instead of freq the flag frqscan can be used to specify an evenly spaced grid of frequency values, e.g. frqscan=0.1,0.2,0.01. The three arguments define the start and end point and the step width of the grid.
top: requests the calculation of ground state third-order properties as e.g. first hyperpolarizability and MCD. The flags for the sop keyword also apply to top. For further information on the properties available, see 10.6.
cpp=on/off: requests the calculation of damped second- or third-order properties with damping factor gamma in a.u. . Must be combined with the sop or top keyword.
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 Hartree-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 Hartree-Fock calculation.)
maxeqsim: set the maximum number of equations that are solved simultaneoulsy (default: 50)

$roothome

2
1
1   8   9   1.00
2
1   2   3   0.50
1   2   4   0.50

Specifies the guess vectors for the excitation calculations. It follows the syntax

<Number of roots>
<Number of components for root #1>
<Spin (1 - alpha, 2- beta)> <#occ (from) MO> <#vrt (to) MO> <coeff.>
...
...
<Number of components for root #2>
...
...

The MO indices should correspond to increasing SCF orbital energy numbering. The data group $excitations with the roothome keyword should also be present in the control file.

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 $\langle\mu|\nu\rangle$
diplen: dipole operator in length gauge: $\langle\mu|r_i^O|\nu\rangle$ 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: $\langle\mu|\nabla_i|\nu\rangle$
(all three components, individual components can be specified with the labels xdipvel, ydipvel, zdipvel).
qudlen: quadrupole operator $\langle\mu|r^O_i r^O_j|\nu\rangle$
(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 $\alpha = \frac{1}{3} \text{tr} M$ and the anisotropy \[\begin{equation*} \beta = \sqrt{\frac{1}{2} \sum_{i=x}^z (M_{ii}-M_{i+1,i+1})^2 +3 \sum_{i=x}^z M_{i,i+1}^2 }\,. \end{equation*}\] Furthermore the traceless quadrupole moment \[\begin{equation*} \Theta_{ij} = \frac{1}{2}\langle 3 r_ir_j -r^2\delta_{ij}\rangle \end{equation*}\] (including nuclear contributions) is given.
angmom: angular momentum $\langle\mu|L^O_i|\nu\rangle$
(all three components, individual components can be specified with the labels xangmom, yangmom, zangmom).
nef: electronic force on nuclei $\langle\mu|\frac{Z_I r_i^I}{{r^I}^3}|\nu\rangle$, 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.

istates=all fstates=all

The specification of initial and final states for transition properties between excited states is mandatory. The syntax is analog to the states option, i.e. either all or a list of of states is required.

$D2-diagnostic

Calculate the double-substitution-based diagnostics $D_2$.

$cc2_natocc

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

$cgrad 1000

Calculate the error functional $\delta_{\mathrm{RI}}$ for the RI approximation of $(ai|bj)$ integrals \[\delta_{\mathrm{RI}} = \frac{1}{4} \frac{|\langle ab || ij \rangle_{exact} - \langle ab || ij \rangle_{\mathrm{RI}} |^2 }{ \epsilon_a - \epsilon_i + \epsilon_b - \epsilon_j }\] 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 1.7).

25.2.23 Keywords for Module ricc2

25.2.23 Keywords for Module `ricc2`