Description

The CIS method keyword requests a calculation on excited states using single-excitation CI (CI-Singles) [Foresman92]. This implementation works for both closed-shell and open-shell systems.

CIS jobs can include the Density keyword. Without options, this keyword causes the population analysis to use the current (CIS) density rather than its default of the Hartree-Fock density. Note that Density cannot be used with CIS(D).

An energy range can be specified for CIS excitation energies using some options found under the procedure-related options below.

CIS(D) is used to request the related CIS(D) method (i.e. the D option) [Head-Gordon94a, Head-Gordon95]. You can also follow a CIS job with a CIS(D) job to compute the excitation energies for additional states (see the examples).

Options

### State Selection Options

#### Singlets

Solve only for singlet excited states. This option only affects calculations on closed-shell systems, for which it is the default.

#### Triplets

Solve only for triplet excited states. This option only affects calculations on closed-shell systems.

#### 50-50

Solve for half triplet and half singlet states. This option only affects calculations on closed-shell systems.

#### Root=N

Specifies the “state of interest” for which the generalized density is to be computed. The default is the first excited state (N=1).

#### NStates=M

Solve for M states (the default is 3). If 50-50 is requested, NStates gives the number of each type of state for which to solve (i.e., the default is 3 singlets and 3 triplets).

Instead of an integer, Read may be specified as this option’s parameter. In this case, the number of states to compute is read from the input stream. This is typically used in EET calculations.

#### Add=N

Read converged states off the checkpoint file and solve for an additional N states. This option implies Read as well. NStates cannot be used with this option.

### Energy Range Options

#### GOccSt=N

Generate initial guesses using only active occupied orbitals N and higher.

#### GOccEnd=N

Generate initial guesses: if N>0, use only the first N active occupied orbitals; if N<0, do not use the highest |N| occupieds.

#### GDEMin=N

Generate guesses having estimated excitation energies ≥ N/1000 eV.

#### DEMin=N

Converge only states having excitation energy ≥ N/1000 eV; if N=-2, read threshold from input; if N<-2, set the threshold to |N|/1000 Hartrees.

#### IFact=N

Specify factor by which the number of states updated during initial iterations is increased.

#### WhenReduce=M

Reduce to the desired number of states after iteration M.

The default for IFact is Max(4,g) where g is the order of the Abelian point group. The default for WhenReduce is 2. A larger value may be needed if there are many states in the range of interest.

### Density-Related Option

#### AllTransitionDensities

Computes the transition densities between every pair of states.

### Procedure- and Algorithm-Related Options

#### 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.

#### Direct

Forces solution of the CI-Singles equation using AO integrals which are recomputed as needed. CIS=Direct should be used only when the approximately 4O^{2}N^{2} words of disk required for the default (MO) algorithm are not available, or for larger calculations (over 200 basis functions).

#### MO

Requests that a CIS calculation use transformed integrals. This was the default for CIS in G09 but is never the default in G16.

#### AO

Forces solution of the CI-Singles equations using the AO integrals, avoiding an integral transformation. The AO basis is seldom an optimal choice, except for small molecules on systems having very limited disk and memory.

#### Conver=N

Sets the convergence calculations to 10^{-N} on the energy and 10^{-(N-2)} on the wavefunction. The default is N=4 for single points and N=6 for gradients.

#### Read

Reads initial guesses for the CI-Singles states off the checkpoint file. Note that, unlike for SCF, an initial guess for one basis set cannot be used for a different one.

#### Restart

Restarts the CI-Singles iterations off the checkpoint file. Also implies SCF=Restart.

#### RWFRestart

Restarts the CI-Singles iterations off the read-write file. Useful when using non-standard routes to do successive CI-Singles calculations.

#### EqSolv

Whether to perform equilibrium or non-equilibrium PCM solvation. NonEqSolv is the default except for excited state optimizations and when the excited state density is requested (e.g., with the Current or All options to the Density keyword).

#### NoIVOGuess

Forces the use of canonical single excitations for the guess. IVOGuess, which uses improved virtual orbitals, is the default.

#### NonAdiabaticCoupling

Requests that the ground-to-excited-state non-adiabatic coupling be computed. NAC is a synonym for this option. NoNonAdiabaticCoupling and NoNAC suppress this behavior. The default is NoNAC when computing energies or energies+gradients because the extra cost is non-trivial. The default is NAC during frequency calculations where the extra cost is negligible.

### Debugging Options

#### ICDiag

Forces in-core full diagonalization of the CI-Singles matrix formed in memory from transformed integrals. This is mainly a debugging option.

#### MaxDiag=N

Limits the submatrix diagonalized in the Davidson procedure to dimension N. This is mainly a debugging option. MaxDavidson is a synonym for this option.

Availability

Energies, analytic gradients, and analytic frequencies for CIS (including open shell systems), and energies for CIS(D).

Related Keywords

Examples

CIS Output. There are no special features or pitfalls with CI-Singles input. Output from a single point CI-Singles calculation resembles that of a ground-state CI or QCI run. An SCF is followed by the integral transformation and evaluation of the ground-state MP2 energy. Information about the iterative solution of the CI problem comes next; note that at the first iteration, additional initial guesses are made, to ensure that the requested number of excited states are found regardless of symmetry. After the first iteration, one new vector is added to the solution for each state on each iteration.

The change in excitation energy and wavefunction for each state is printed for each iteration (in the #P output):

Iteration 3 Dimension 27 Root 1 not converged, maximum delta is 0.002428737687607 Root 2 not converged, maximum delta is 0.013107675296678 Root 3 not converged, maximum delta is 0.030654755631835 Excitation Energies [eV] at current iteration: Root 1 : 3.700631883679401 Change is -0.001084398684008 Root 2 : 7.841115226789293 Change is -0.011232152003400 Root 3 : 8.769540624626156 Change is -0.047396173133051

The iterative process can end successfully in two ways: generation of only vanishingly small expansion vectors, or negligible change in the updated wavefunction.

When the CI has converged, the results are displayed, beginning with this banner:

***************************************************************** Excited States From <AA,BB:AA,BB> singles matrix: *****************************************************************

The transition dipole moments between the ground and each excited state are then tabulated. Next, the results on each state are summarized, including the spin and spatial symmetry, the excitation energy, the oscillator strength, and the largest coefficients in the CI expansion (use IOp(9/40=N) to request more coefficients: all that are greater than 10^{-N}):

Excitation energies and oscillator strengths: Symmetry, excitation energy, oscillator strength Excited State 1: Singlet-A' 3.7006 eV 335.03 nm f=0.0008 CI expansion coeffs. for each excitation: 8 -> 9 0.69112 Orbital 8 to 9 This state for opt. and/or second-order corr. This is the state of interest. Total Energy, E(CIS) = -113.696894498 CIS energy is repeated here for convenience.

CI expansion coefficients give the importance of excited determinants in the excited state wavefunction.

Normalization. For closed shell calculations, the sum of the squares of the expansion coefficients is normalized to total 1/2 (as the beta coefficients are not shown). For open shell calculations, the normalization sum is 1.

Finding Additional States. The following route will read the CIS results from the checkpoint file and solve for 6 additional states beyond those predicted in the previous calculation:

# CIS=(Read,Root=2,Add=6)

The CIS method keyword requests a calculation on excited states using single-excitation CI (CI-Singles) [Foresman92]. This implementation works for both closed-shell and open-shell systems.

CIS jobs can include the Density keyword. Without options, this keyword causes the population analysis to use the current (CIS) density rather than its default of the Hartree-Fock density. Note that Density cannot be used with CIS(D).

An energy range can be specified for CIS excitation energies using some options found under the procedure-related options below.

CIS(D) is used to request the related CIS(D) method (i.e. the D option) [Head-Gordon94a, Head-Gordon95]. You can also follow a CIS job with a CIS(D) job to compute the excitation energies for additional states (see the examples).

### State Selection Options

#### Singlets

Solve only for singlet excited states. This option only affects calculations on closed-shell systems, for which it is the default.

#### Triplets

Solve only for triplet excited states. This option only affects calculations on closed-shell systems.

#### 50-50

Solve for half triplet and half singlet states. This option only affects calculations on closed-shell systems.

#### Root=N

Specifies the “state of interest” for which the generalized density is to be computed. The default is the first excited state (N=1).

#### NStates=M

Solve for M states (the default is 3). If 50-50 is requested, NStates gives the number of each type of state for which to solve (i.e., the default is 3 singlets and 3 triplets).

Instead of an integer, Read may be specified as this option’s parameter. In this case, the number of states to compute is read from the input stream. This is typically used in EET calculations.

#### Add=N

Read converged states off the checkpoint file and solve for an additional N states. This option implies Read as well. NStates cannot be used with this option.

### Energy Range Options

#### GOccSt=N

Generate initial guesses using only active occupied orbitals N and higher.

#### GOccEnd=N

Generate initial guesses: if N>0, use only the first N active occupied orbitals; if N<0, do not use the highest |N| occupieds.

#### GDEMin=N

Generate guesses having estimated excitation energies ≥ N/1000 eV.

#### DEMin=N

Converge only states having excitation energy ≥ N/1000 eV; if N=-2, read threshold from input; if N<-2, set the threshold to |N|/1000 Hartrees.

#### IFact=N

Specify factor by which the number of states updated during initial iterations is increased.

#### WhenReduce=M

Reduce to the desired number of states after iteration M.

The default for IFact is Max(4,g) where g is the order of the Abelian point group. The default for WhenReduce is 2. A larger value may be needed if there are many states in the range of interest.

### Density-Related Option

#### AllTransitionDensities

Computes the transition densities between every pair of states.

### Procedure- and Algorithm-Related Options

#### 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.

#### Direct

Forces solution of the CI-Singles equation using AO integrals which are recomputed as needed. CIS=Direct should be used only when the approximately 4O^{2}N^{2} words of disk required for the default (MO) algorithm are not available, or for larger calculations (over 200 basis functions).

#### MO

Requests that a CIS calculation use transformed integrals. This was the default for CIS in G09 but is never the default in G16.

#### AO

Forces solution of the CI-Singles equations using the AO integrals, avoiding an integral transformation. The AO basis is seldom an optimal choice, except for small molecules on systems having very limited disk and memory.

#### Conver=N

Sets the convergence calculations to 10^{-N} on the energy and 10^{-(N-2)} on the wavefunction. The default is N=4 for single points and N=6 for gradients.

#### Read

Reads initial guesses for the CI-Singles states off the checkpoint file. Note that, unlike for SCF, an initial guess for one basis set cannot be used for a different one.

#### Restart

Restarts the CI-Singles iterations off the checkpoint file. Also implies SCF=Restart.

#### RWFRestart

Restarts the CI-Singles iterations off the read-write file. Useful when using non-standard routes to do successive CI-Singles calculations.

#### EqSolv

Whether to perform equilibrium or non-equilibrium PCM solvation. NonEqSolv is the default except for excited state optimizations and when the excited state density is requested (e.g., with the Current or All options to the Density keyword).

#### NoIVOGuess

Forces the use of canonical single excitations for the guess. IVOGuess, which uses improved virtual orbitals, is the default.

#### NonAdiabaticCoupling

Requests that the ground-to-excited-state non-adiabatic coupling be computed. NAC is a synonym for this option. NoNonAdiabaticCoupling and NoNAC suppress this behavior. The default is NoNAC when computing energies or energies+gradients because the extra cost is non-trivial. The default is NAC during frequency calculations where the extra cost is negligible.

### Debugging Options

#### ICDiag

Forces in-core full diagonalization of the CI-Singles matrix formed in memory from transformed integrals. This is mainly a debugging option.

#### MaxDiag=N

Limits the submatrix diagonalized in the Davidson procedure to dimension N. This is mainly a debugging option. MaxDavidson is a synonym for this option.

Energies, analytic gradients, and analytic frequencies for CIS (including open shell systems), and energies for CIS(D).

CIS Output. There are no special features or pitfalls with CI-Singles input. Output from a single point CI-Singles calculation resembles that of a ground-state CI or QCI run. An SCF is followed by the integral transformation and evaluation of the ground-state MP2 energy. Information about the iterative solution of the CI problem comes next; note that at the first iteration, additional initial guesses are made, to ensure that the requested number of excited states are found regardless of symmetry. After the first iteration, one new vector is added to the solution for each state on each iteration.

The change in excitation energy and wavefunction for each state is printed for each iteration (in the #P output):

Iteration 3 Dimension 27 Root 1 not converged, maximum delta is 0.002428737687607 Root 2 not converged, maximum delta is 0.013107675296678 Root 3 not converged, maximum delta is 0.030654755631835 Excitation Energies [eV] at current iteration: Root 1 : 3.700631883679401 Change is -0.001084398684008 Root 2 : 7.841115226789293 Change is -0.011232152003400 Root 3 : 8.769540624626156 Change is -0.047396173133051

The iterative process can end successfully in two ways: generation of only vanishingly small expansion vectors, or negligible change in the updated wavefunction.

When the CI has converged, the results are displayed, beginning with this banner:

***************************************************************** Excited States From <AA,BB:AA,BB> singles matrix: *****************************************************************

The transition dipole moments between the ground and each excited state are then tabulated. Next, the results on each state are summarized, including the spin and spatial symmetry, the excitation energy, the oscillator strength, and the largest coefficients in the CI expansion (use IOp(9/40=N) to request more coefficients: all that are greater than 10^{-N}):

Excitation energies and oscillator strengths: Symmetry, excitation energy, oscillator strength Excited State 1: Singlet-A' 3.7006 eV 335.03 nm f=0.0008 CI expansion coeffs. for each excitation: 8 -> 9 0.69112 Orbital 8 to 9 This state for opt. and/or second-order corr. This is the state of interest. Total Energy, E(CIS) = -113.696894498 CIS energy is repeated here for convenience.

CI expansion coefficients give the importance of excited determinants in the excited state wavefunction.

Normalization. For closed shell calculations, the sum of the squares of the expansion coefficients is normalized to total 1/2 (as the beta coefficients are not shown). For open shell calculations, the normalization sum is 1.

Finding Additional States. The following route will read the CIS results from the checkpoint file and solve for 6 additional states beyond those predicted in the previous calculation:

# CIS=(Read,Root=2,Add=6)

Last updated on: 05 January 2017. [G16 Rev. C.01]