CIS / TDDFT

TeraChem computes excited states by linear response from a single-determinant SCF reference.¹² A single family of keywords (all prefixed cis) drives three closely related methods that differ only in the reference and the response kernel:

You write	Reference (`method`)	Method obtained
`cis yes`	`hf`	CIS (configuration interaction singles)
`cis yes`	a DFT functional (`pbe0`, `wb97x`, …)	TDA-DFT (Tamm–Dancoff-approximated TDDFT)
`cis yes` + `rpa yes`	a DFT functional	full TDDFT (Casida / random-phase approximation)

CIS and TDA-DFT solve the Tamm–Dancoff eigenvalue problem

\[ \mathbf{A}\,\mathbf{X} = \omega\,\mathbf{X}, \]

where \(\mathbf{A}\) is the orbital-Hessian block coupling singly-excited configurations. Full TDDFT (rpa yes) instead solves the larger non-Hermitian problem

\[ \begin{pmatrix} \mathbf{A} & \mathbf{B} \\ -\mathbf{B} & -\mathbf{A} \end{pmatrix} \begin{pmatrix} \mathbf{X} \\ \mathbf{Y} \end{pmatrix} = \omega \begin{pmatrix} \mathbf{X} \\ \mathbf{Y} \end{pmatrix}, \]

which adds the de-excitation coupling block \(\mathbf{B}\). The Tamm–Dancoff approximation (\(\mathbf{B}=0\))³ is the default and is usually more robust near conical intersections and for triplet instabilities, at a small cost in excitation-energy accuracy.

Because the reference determinant is what distinguishes the methods, the same cis* solver, gradient, coupling, and property keywords apply to all three.

Quick start

The minimum needed to request excited states is the master switch plus the number of states:

cis           yes
cisnumstates  8       # number of excited states to solve for

Set method hf for CIS or a DFT functional for TDA-DFT. By default TeraChem solves for singlet states (on a closed-shell reference) and prints excitation energies, oscillator strengths, and transition dipole moments.

Example 1: restricted CIS

A closed-shell CIS gradient calculation on thioformaldehyde. The Hartree–Fock reference makes this CIS; cistarget 5 selects the state whose gradient is computed:

cis_grad.in

coordinates     coord.xyz
basis           def2-svp
method          hf
charge          0
spinmult        1
maxit           100
threall         1e-14
convthre        1.0e-6

cis             yes
cisnumstates    8
cisalgorithm    davidson
cisconvtol      1e-6
cistransdipole  yes
cistarget       5
cismaxiter      30

# excited-state properties
cisntos         yes
cisnos          yes
cisattachdetach yes

run             gradient

This produces 8 CIS singlet states and the analytic gradient on the 5th excited state, along with natural transition orbitals, natural orbitals, and attachment/detachment densities (written as .molden files).

Example 2: TDA-DFT

Switching the reference to a DFT functional turns the identical input into a TDA-DFT calculation. Here pbe0 is used:

tdadft_grad.in

coordinates     coord.xyz
basis           def2-svp
method          pbe0
sphericalbasis  yes
charge          0
spinmult        1
maxit           100
threall         1e-14
convthre        1.0e-4

cis             yes
cisnumstates    8
cisalgorithm    davidson
cistransdipole  yes
cistarget       5
cismaxiter      30

run             gradient

Everything about the excited-state setup is the same as for CIS — only method changed.

Example 3: full TDDFT (beyond Tamm–Dancoff)

Adding rpa yes solves the full Casida equations instead of the Tamm–Dancoff problem:

tddft_energy.in

coordinates     coord.xyz
basis           def2-svp
method          wb97x
charge          0
spinmult        1
threall         1e-14
convthre        1.0e-6

cis             yes
rpa             yes        # full TDDFT instead of TDA
cisnumstates    4
cisalgorithm    davidson
cisconvtol      1e-6

run             energy

TDA vs. full TDDFT

Full TDDFT can give lower (sometimes spuriously imaginary) triplet excitation energies when the reference has a triplet instability; the Tamm–Dancoff approximation (the default, without rpa yes) avoids this and is generally preferred for excited-state dynamics and geometry optimization.

Variants

Triplet states

By default TeraChem solves for states of the same multiplicity as the reference (singlets for a closed-shell reference). To target triplets from a closed-shell reference, set cismult 3:

cis           yes
cismult       3        # solve for triplet excited states
cisnumstates  4

To obtain both singlets and triplets in a single run, keep cismult 1 (singlets) and request triplets in addition with cisnumtriplet:

cis           yes
cismult       1
cisnumstates  4        # singlets
cisnumtriplet 4        # triplets, computed in the same calculation

Open-shell references: UCIS and ROCIS

For open-shell systems (radicals, high-spin states) choose an unrestricted or restricted-open-shell reference. cis yes then automatically produces the corresponding open-shell linear-response method:

method uhf (or an unrestricted DFT functional) → UCIS / U-TDA-DFT
method rohf → ROCIS

ucis_grad.in

coordinates     coord.xyz
basis           def2-svp
method          uhf        # use rohf for ROCIS instead
charge          0
spinmult        3
threall         1.0e-14
convthre        1.0e-8
precision       mixed

cis             yes
cisnumstates    5
cisguessvecs    30
cismax          500
cismaxiter      500
cisconvtol      1.0e-6
cistarget       2
cisntos         yes
cisattachdetach yes
cisnos          yes

cphfalgorithm   diis
cphftol         1.0e-6
cphfiter        1000

run             gradient

Spin-flip TDDFT / CIS

Spin-flip excitations start from a high-spin reference (e.g. an \(M_S=1\) triplet) and reach lower-multiplicity target states (e.g. the open-shell singlet and the \(M_S=0\) triplet component) by flipping a single spin. This is particularly useful for diradicals and bond dissociation, where the spin-flip target states are described in a balanced way.⁴

Enable it with spinflip yes on a UHF or ROHF high-spin reference:

sf_tddft_grad.in

coordinates     butadiene.xyz
basis           6-31g**
method          uhf        # or rohf
charge          0
spinmult        3          # high-spin reference

cis             yes
spinflip        yes
cisnumstates    5
cisguessvecs    20
cismax          500
cismaxiter      500
cisconvtol      1.0e-6
cistarget       2
cisnos          yes

cphfalgorithm   diis
cphftol         1.0e-6
cphfiter        1000

run             gradient

Note

With spinflip yes, cistarget counts the spin-flip roots produced from the high-spin reference (the lowest root is typically the spin-flipped ground state, not a true excited state). Inspect the printed \(\langle \hat S^2 \rangle\) values to identify the multiplicity of each state.

Excited-state gradients and dynamics

Set cistarget to the (1-based) index of the excited state of interest and choose the appropriate run mode. Analytic gradients are evaluated through the coupled-perturbed equations (CPHF/CPKS), controlled by the cphf* keywords:

`run` value	What it does
`energy`	Excitation energies, oscillator strengths, and properties
`gradient`	Analytic gradient on state `cistarget`
`minimize`	Geometry optimization on state `cistarget`
`ts`	Transition-state search on state `cistarget`
`md`	Born–Oppenheimer dynamics on state `cistarget`
`coupling`	Nonadiabatic couplings (see below)
`conical`	Minimum-energy conical-intersection optimization — see CIOpt

cistarget 0 selects the ground state (the underlying SCF state). Analytic excited-state gradients are not available together with an orbital-restricted active space (see Orbital-restricted CIS).

Nonadiabatic couplings

Derivative (nonadiabatic) coupling vectors between two states are requested with run coupling and the pair nacstate1 / nacstate2. The coupled-perturbed CIS response equations are controlled by the cpcis* keywords:

nac.in

coordinates     coord.xyz
basis           6-31g
method          bhandhlyp
dftgrid         1
charge          0
spinmult        1

cis             yes
cismult         3
cisnumstates    4
cisalgorithm    davidson
cistransdipole  yes
cistarget       2
cismaxiter      30
cisconvtol      1e-6

nacstate1       2          # couple states 2 and 3
nacstate2       3

run             coupling

State indices 0 refers to the ground state, so nacstate1 0 / nacstate2 1 gives the \(S_0/S_1\) coupling. Numerical couplings are available with run numcoupling.

Excited-state properties

Most properties are written for every state (and every transition); some are on by default. The most commonly used:

Keyword	Default	Description
`cistransdipole`	yes	Transition dipole moments and oscillator strengths between the ground and excited states
`cisntos`	no	Natural transition orbitals for each state (`nto_*.molden`)
`cisnos`	no	State natural orbitals (`no_*.molden`)
`cisattachdetach`	no	Attachment/detachment densities (`ad_*.molden`)
`cistransdensity`	no	Transition densities
`cisdiffdensity`	no	Difference (excited − ground) densities
`cischarges`	no	Atomic partial charges for the excited states
`cisunrelaxdipole`	yes	Unrelaxed excited-state dipole moments
`cisrelaxdipole`	no	Orbital-relaxed excited-state dipole moments (requires the CPHF solve)
`cisdipolederiv`	no	Excited-state dipole derivatives (e.g. for IR-like intensities)
`cistransdipolederiv`	no	Transition-dipole derivatives
`cisprintcivec`	yes	Print the dominant CI amplitudes for each state
`cisprintthresh`	0.1	Amplitude print threshold for `cisprintcivec`

Orbital-restricted CIS for XAS

Excitations can be restricted to start from a chosen set of (e.g. core) orbitals, which is useful for X-ray absorption / core-excited spectra. This is enabled with cisrestrictorbitals yes together with cisactiveorbitals (or the spin-resolved cisactivealphaorbitals / cisactivebetaorbitals).

Warning

Orbital-restricted CIS is a non-production feature: analytic gradients are not available when an orbital restriction is active. Use it for single-point excitation energies and spectra only.

Summary of keywords

Master switches

Keyword	Type	Default	Description
`cis`	bool	no	Master switch — activates CIS / TDA-DFT (method set by `method`)
`rpa`	bool	no	Solve the full TDDFT (RPA) equations instead of the Tamm–Dancoff approximation
`rocis`	bool	no	Explicitly request restricted-open-shell CIS (also obtained from `method rohf` + `cis yes`)
`spinflip`	bool	no	Spin-flip excitations from a high-spin reference
`cisspinorbit`	bool	no	Include spin–orbit coupling between the computed states

States and solver (Davidson)

Keyword	Type	Default	Description
`cisnumstates`	int	1	Number of excited states (roots) to solve for
`cismult`	int	from reference	Multiplicity of the target states (`1` singlet, `3` triplet)
`cisnumtriplet`	int	0	Additional triplet states to compute alongside singlets (only with `cismult 1`)
`cistarget`	int	0	State for gradients/properties (0 = ground, 1 = first excited, …)
`cisalgorithm`	string	davidson	Eigensolver (`davidson`; `debug` for diagnostics)
`cisguessvecs`	int	= `cisnumstates`	Number of initial Davidson guess vectors
`cismax`	int	10 × `cisnumstates`	Maximum Davidson subspace dimension
`cismaxiter`	int	20	Maximum Davidson iterations
`cisconvtol`	float	1.0e-4	Davidson eigenvector convergence tolerance
`ciscollapse`	int	2	Vectors retained per root when the subspace is collapsed

Response equations (gradients and couplings)

Keyword	Type	Default	Description
`cphftol`	float	1.0e-4	CPHF/CPKS convergence tolerance (excited-state gradients)
`cphfiter`	int	20	Maximum CPHF iterations
`cphfalgorithm`	string	diis	CPHF solver (`diis`, `inc_diis`, `cg`, `precon_cg`, `jacobi`, `inc_jacobi`)
`cpcistol`	float	1.0e-4	CP-CIS convergence tolerance (nonadiabatic couplings)
`cpcisiter`	int	20	Maximum CP-CIS iterations
`cpcisalgorithm`	string	diis	CP-CIS solver (`diis`, `inc_diis`)
`nacstate1`	int	—	First state of a nonadiabatic-coupling pair
`nacstate2`	int	—	Second state of a nonadiabatic-coupling pair

Orbital restriction (XAS)

Keyword	Type	Default	Description
`cisrestrictorbitals`	bool	no	Restrict excitations to a chosen orbital window
`cisactiveorbitals`	string	—	Active (occupied) orbitals excitations originate from
`cisactivealphaorbitals`	string	—	As above, alpha spin only
`cisactivebetaorbitals`	string	—	As above, beta spin only

References

A. Dreuw and M. Head-Gordon, Single-Reference ab Initio Methods for the Calculation of Excited States of Large Molecules, Chem. Rev. 105, 4009 (2005). ↩
M. E. Casida, in Recent Advances in Density Functional Methods, Vol. 1 (World Scientific, 1995), p. 155. ↩
S. Hirata and M. Head-Gordon, Time-dependent density functional theory within the Tamm–Dancoff approximation, Chem. Phys. Lett. 314, 291 (1999). ↩
Y. Shao, M. Head-Gordon, and A. I. Krylov, The spin–flip approach within time-dependent density functional theory, J. Chem. Phys. 118, 4807 (2003). ↩