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*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. `(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*D*_{1}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*D*_{1}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*,*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 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
^{-}. If not given, a default value is used, which is chosen as max(10^{-}, 10^{-}, 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^{-}(default: 3). `thrdiis`-

threshold ( 10^{-}) 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
^{-}. If not given in the`$response`data group, a default value is used, which is chosen as max(10^{-},

10^{-}, 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^{-}. `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^{-}. 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^{-}. 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.)

`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}_{i}*r*^{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*= tr*M*and the anisotropy*β*= .

Furthermore the traceless quadrupole moment*Θ*_{ij}= 〈3*r*_{i}*r*_{j}-*r*^{2}*δ*_{ij}〉

(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*||*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*D*_{2}. `$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}=`$cbas`. The results are written to`$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).