The keyword selects the Symmetry Adapted Cluster/Configuration Interaction (SAC-CI) methods of Nakatsuji and coworkers [Nakatsuji78, Nakatsuji79, Nakatsuji79a, Nakatsuji91, Nakatsuji91a, Nakatsuji93, Nakatsuji97, Nakajima97, Nakatsuji97a, Hasegawa98, Hasegawa98a, Nakajima99, Ishida01, Ishida01a, Ehara02, Toyota02, Toyota03, Nakatsuji07, Fukuda08, Nakatani07, Nakatani07a, Fujimoto09, Miyahara13, Miyahara13a]. For detailed information on this method, consult the SAC-CI documentation available at the following web site: www.qcri.or.jp/sacci/. For review articles, see [Nakatsuji97, Nakatsuji97a, Ehara05].

SAC-CI jobs must specify a reference state for the subsequent excited states calculations. For closed shell systems, the default RHF wavefunction used by SAC-CI is appropriate. For open shell ground states, you must either select an ROHF ground state wavefunction by including ROHF in the route section in addition to SAC-CI, or you must specify a closed shell state for the ground state calculation using the AddElectron or SubElectron option. See the examples for more information.

### Spin State Options

#### Singlet=(additional-options)

Specifies that singlet states are to be calculated. The parenthesized list of suboptions specifies the desired states and other calculation parameters. Other spin state selection options are CationDoublet (Doublet is a synonym), AnionDoublet, Triplet, Quartet, Quintet, Sextet and Septet. More than one spin state may be specified.

In the options that follow, SpinState is replaced by the name of the desired spin state.

#### SpinState=(NState=(i_{1},i_{2},…))

Sets the number of states of the specified type to be calculated for the various irreducible representations of the molecule’s point group. Up to eight values may be specified, depending on the molecular symmetry (e.g., 8 for D_{2h}, 4 for C_{2v}, and so on). The shorthand form NState=N specifies a value of N for each irreducible representation. Degeneracies are handled by assuming the closest linear symmetry (e.g., D_{2} for T_{d}).

#### SpinState=(Density)

Calculate unrelaxed density matrices and perform Mulliken population analysis for all computed SAC-CI states of spin SpinState. See the examples for more information.

#### SpinState=(SpinDensity)

Calculate spin density matrices for all computed SAC-CI states of spin SpinState. Implies the FullActive option as well.

#### SpinState=(NoTransitionDensity)

By default, the transition density and oscillator strength are calculated between the SAC ground state and the SAC-CI singlet excited states when SpinState is Singlet, and between the lowest SAC-CI states and SAC-CI excited states for other spin states. NoTransitionDensity disables these calculations for the corresponding spin state.

#### TargetState=(SpinState=s, Symmetry=m, Root=n)

Specifies the target state for a geometry optimization or a gradient calculation, or for use with the Density keyword. S is the keyword indicating its spin multiplicity (i.e., Singlet, Doublet, etc.), m is the irreducible representation number of its point group, and n is the solution number in the desired spin state (determined by a previous energy calculation).

#### AddElectron

Add one electron to the open shell reference SCF configuration. This is the default for such systems for CationDoublet, Doublet, Quartet and Sextet.

#### SubElectron

Subtract one electron from the open shell reference SCF configuration. This is the default for such systems for AnionDoublet.

#### TransitionFrom=(SpinState=s, Symmetry=m, Root=n)

Specifies the initial state for calculating transition density matrices. S is the keyword indicating its spin multiplicity (i.e., Singlet, Doublet, etc.), m is the irreducible representation number of its point group, and n is the solution number in the desired spin state (as for TargetState above).

#### AllProperties

Calculate multipole moments through hexadecapole, all nth moments to the 4th moment, all electrostatic properties and the diamagnetic terms (shielding and susceptibility). This option applies to all spin states which specify the Density suboption.

#### NoProperty

Don’t calculate any molecular properties.

#### SelectCISOnly

Terminate the calculation after the CIS initial guess has been calculated. You can use this option to determine the state number of a particular state in which you are interested (e.g., for TargetState). See the examples for an alternative method.

#### SACOnly

Performs only the calculation for the reference state and does not compute any excited states.

### Additional Options for Expert Users

For this set of options, SpinState below is replaced by the name of the desired spin state.

#### SpinState=(MaxR=N)

Set the maximum excitation level to N.

#### SpinState=(NonVariational)

Solve the SAC-CI equations for non-symmetric matrices. Variational proceeds by diagonalizing symmetrized matrices, and it is the default. Note that this option only applies to the excited state portion of the calculation (the ground state calculation always uses a nonvariational procedure).

#### SpinState=(InCoreDiag)

Force use of the in-core algorithm.

#### SpinState=(Iterative=item)

Force the use of an iterative algorithm. Item specifies the initial guess type: SInitial for CIS and SDInitial for CISD.

#### Direct

Requests to use the direct algorithm for the SAC/SAC-CI SD-R calculations. Direct is not compatible with General-R, WithoutR2S2, FullUnlinked, InCoreDiag, and InCoreSAC. The direct SAC-CI code uses different values of internal thresholds, which correspond to the conventional SAC-CI calculations with NoUnlinkedSelection keywords. Therefore, the results obtained with the direct SAC-CI code are usually different from the results with the conventional SAC-CI code. The direct SAC-CI code is efficient and therefore strongly recommended. (available in Rev. B01 and later) [Fukuda08].

#### FC

All frozen core options are available with this keyword; a frozen core calculation is the default. See the discussion of the FC options for full information.

In general, the size of the active space greatly affects the accuracy of SAC-CI calculations. For this reason, using a full orbital window is recommended. Full is the default for geometry optimizations and gradient calculations.

#### LMO=type

Use the specified type of localized MO as reference orbitals. The available types are PM (Pipek-Mezey) and Boys.

#### Window=(M[,N])

Means that the SAC/SAC-CI calculation is done within the M-th to N-th active orbital space (M < N in the energy order). Window=(M[,N]) is a synonym for ReadWindow=(M[,N]). If spin densities at the nuclei are of interest, as for Electron Spin Resonance or hyperfine splitting, then the core orbitals must be included in the window.

#### CorePrWindow=(M,N)

Activates the calculation of core-excited/core-ionized states and specifies core orbitals from which an electron is excited or ionized in the core-electron processes; M and N specify the range of core orbitals. This keyword is used with the FullActive or Window keyword to include core-orbitals in the active space (available in Rev. C01 and later).

#### MacroIteration=N

Requests the use of N macroiterations within an optimization step. The default value of N is 0.

#### InCoreSAC

For solution of the SAC equations using the in-core algorithm.

#### MaxItDiag=N

Set the maximum number of diagonalization iterations. The default is 64 and the maximum is 999.

#### MaxItSAC=N

Set the maximum number of iterations for solving the SAC equations. The default is 999.

#### MaxItLin=N

Set the maximum number of iterations allowed to solve the SAC linear equations. The maximum is 999.

#### DConvDiag=M

Set the diagonalization energy convergence criteria to 10^{-M}.

#### DConvSAC=M

Set the energy convergence criteria to 10^{-M} when solving the SAC equations.

#### SD-R

Perform the calculation using singles and doubles linked excitation operators. This is the default.

#### General-R

Perform the calculation including linked excitation operators through sextuples.

#### LevelOne

Set the thresholds for selection of the double excitation operators to the lowest recommended level. LevelThree is the most accurate level, and it is the default. LevelTwo is intermediate in accuracy between the other two levels.

#### WithoutDegeneracy

By default, perturbation selection is performed so that degeneracies are retained. This option suppresses this test, resulting in reduced computational requirements. Use of this option is not recommended for production use.

#### NoLinkedSelection

Disables perturbation selection thresholds for linked operators (i.e., all operators are included).

#### NoUnlinkedSelection

Disables perturbation selection thresholds for unlinked operators (i.e., all operators are included).

#### FullUnlinked

Include all types of unlinked terms. Forces the use of the in-core algorithm.

In order to include all terms, all three of NoLinkedSelection, NoUnlinkedSelection, and FullUnlinked are required, currently at a considerable performance penalty.

#### WithoutR2S2

Ignore R2S2 unlinked integrals. This option results in a tradeoff between decreased accuracy and computational requirements.

#### EgOp

Generate quadruple and higher-order linked operators in the General-R scheme via the exponential generation algorithm. This is the default for single point energy calculations. The highest order excitation level is specified via the MaxR option (up to a maximum of 6). Perturbation selection thresholds are set via the LevelOne, LevelTwo and LevelThree options.

#### FullRGeneration

Generate all higher-order linked operators in the General-R scheme up to MaxR=4 and then perform perturbation selection as above. This is the default for gradient calculations and geometry optimizations.

These options are used to ensure consistency between all points in multipoint calculation types like potential energy surface scans. The Scan calculation must be performed three times: at the first point with BeforeGSUM, then at some or all subsequent points with CalcGSUM and then finally at all points with AfterGSUM. The actual results are provided by the final calculation. This procedure is only valid for singlet, triplet, ionized and electron-attached states, and it is not compatible with the General-R option.

#### BeforeGSUM

Initialize a series of linked calculations. Use this option in a calculation at the first point.

#### CalcGSUM

Collect data and determine the thresholds and operator selections at specified points in order to form a consistent set which can then be used at every point.

#### AfterGSUM

Perform SAC-CI calculations at each point using the GSUM data collected previously with the CalcGSUM option.

These options can be used to increase the program default settings after a failed job has indicated that a resource shortfall was the problem.

#### MaxR2Op=N

Set the maximum number of R2 operators after perturbation selection to N. The default is 100,000.

#### MaxEgOp=N

Set the maximum number of operators in the General-R method to N. The default is 5,000.

Energy, analytical energy gradient, geometry optimization, and numerical frequencies.

Geometry optimizations default to using a full window. Specifying a different frozen core option for an optimization will result in numerical gradient calculations and correspondingly poorer performance.

If you want to locate the lowest two singlet excited states, you could use a route like the following:

# SAC-CI=(Singlet=(NState=8))/6-31G(d) NoSymm …

This will search for 8 singlet states, ignoring symmetry. The two lowest excited states will probably be among those found by the calculation.

Alternatively, you could use the following route:

# SAC-CI=(Singlet=(NState=4))/6-31G(d) …

This calculation will locate the lowest four singlet excited states for each irreducible representation.

To specify the desired number of singlet excited states for each irreducible representation for a molecule with C_{2v} symmetry, use a route like this one:

# SAC-CI=(Singlet=(NState=(2,2,1,2)))/6-31G(d) …

Direct SAC-CI.To use the direct SAC-CI code, use the following route:

# SAC-CI=(Direct,Singlet=(…),…)/6-31G(d) …

Locating States with an Inexpensive Initial Calculation. You can use a preliminary, lower-accuracy calculation in order to locate a desired excited state at reduced computational cost. For example, the following route will locate 4 singlet excited states of each symmetry type:

# SAC-CI=(Singlet=(NState=4),LevelOne)/6-31G(d) …

This job could be followed by a normal (LevelThree) calculation for the state(s) of interest. For example:

# SAC-CI=(Singlet=(1,0,1,0))/6-31G(d) …

Calculations on Open Shell Systems. To predict excited states for vinyl radical, a neutral doublet radical, you could use a route like the following:

# ROHF/6-31G(d) SAC-CI=(Doublet=(NState=3),Quartet=(NState=3)) …

This specifies the use of an ROHF wavefunction for the ground state, and it computes three doublet and three quartet excited states for each irreducible representation. You could use a similar approach for the triplet ground state of methylene.

Geometry Optimizations. To optimize a specific excited state, use the TargetState option:

# Opt SAC-CI=(Singlet=(Nstate=4),
TargetState=(SpinState=Singlet,Symmetry=1,Root=2))/6-31G(d) …

Computing Densities and Molecular Properties. To compute the unrelaxed density and population analysis for all predicted excited states, use a route like this one:

# SAC-CI=(Singlet=(…,Density),Triplet=(…,Density))/6-31G(d) …

If you wanted to compute the unrelaxed density and population analysis only for the triplet states, then you would omit the Density suboption to the Singlet option.

To compute the relaxed density and population analysis for only one specified state, use a route like the following:

# SAC-CI=(Singlet=(NState=4),TargetState=(…)) Density=Current …

Note that this job will be much more computationally expensive than the previous one as it requires a full gradient calculation.

SAC-CI Output. SAC-CI calculations produce a table like the following for each requested spin state (this example is for singlet states):

--------------------------------------------------------------------
Transition dipole moment of singlet state from SAC ground state
--------------------------------------------------------------------
Symmetry Sol Excitation Transition dipole moment (au) Osc.
energy (eV) X Y Z strength
--------------------------------------------------------------------
A1 0 0.0 Excitations are from this state.
A1 1 8.7019 0.0000 0.0000 0.4645 0.0460
A1 2 18.9280 0.0000 0.0000 -0.4502 0.0940
A1 3 18.0422 0.0000 0.0000 -0.8904 0.3505
A1 4 18.5153 0.0000 0.0000 0.0077 0.0000
A2 1 7.1159 0.0000 0.0000 0.0000 0.0000
A2 2 18.2740 0.0000 0.0000 0.0000 0.0000
B1 1 1.0334 -0.2989 0.0000 0.0000 0.0023
B1 2 18.7395 -0.6670 0.0000 0.0000 0.2042
B1 3 22.1915 -0.1500 0.0000 0.0000 0.0122
B1 4 15.8155 0.8252 0.0000 0.0000 0.2639
B2 1 11.0581 0.0000 0.7853 0.0000 0.1671
B2 2 15.6587 0.0000 1.5055 0.0000 0.8696
B2 3 24.6714 0.0000 -0.7764 0.0000 0.3644
B2 4 23.5135 0.0000 -0.1099 0.0000 0.0070
---------------------------------------------------------------------

Note that the various excited states are grouped by symmetry type—and not in order of increasing energy—in the output.