tddft: time-dependent density functional theory

Time dependent DFT/HF calculation. Support Full TDDFT, TDA and RPA.

Quick guides

The following examples give the minimal inputs for starting TD-DFT calculations.

1. Closed-shell Systems : R-TD-DFT

2. Open-shell Systems : U-TD-DFT and spin-adapted TD-DFT for spin-conserving excitations

3. TD-DFT with spin-flip calculations

4. Open-shell Systems : Spin-flip TD-DFT for spin-flip excitations

5. TD-DFT with SOC

6. TD-DFT with SOC: open-shell systems

7. TD-DFT with SOC: Kramers pairs

8. Excitation analyze based on molecular fragments

9. Nto analyze

10. Alternative of TD-DFT: particle-particle TDA (pp-TDA) based properties

11. Plot Gaussian-broadened spectra

General keywords

imethod

  imethod 1, R-TDDFT, start from RKS
  imethod 2, U-TDDFT, start from UKS or ROKS
  imethod 3, X-TDDFT, start from ROKS (deprecated; please use imethod=2, itest=1 and icorrect=1 for X-TDDFT, vide infra)

isf

  Spin flip TDDFT. 
  isf 0, do not flip
  isf 1, spin flip up (when imethod=2), spin-conserving triplet calculation (when imethod=1)
  isf -1, spin flip down

itda

  itda 0, full TDDFT, do not use TDA
  itda 1, TDA

ialda

  ialda=0: full non-collinear kernel (default; recommended for isf=0 single point energies)
  ialda=1: non-collinear ALDA kernel
  ialda=2: non-collinear ALDA0 kernel (recommended for isf=1 or isf=-1 single point energies)
  ialda=3: full non-collinear kernel but computed from spin-averaged density
  ialda=4: full collinear kernel (mandatory for spin-flip TD-DFT gradient and NAC)

itest,icorrect

itest=1;icorrect=1 must be set for X-TD-DFT using the U-TD-DFT subroutines.

itrans

itrans=1: transform the final eigenvector in U-TD-DFT from the spin-orbital based representation to spin-adapted basis, e.g., CV(0) and CV(1). This only makes sense when ROKS reference is used.

iact,elw,eup

iact = 1: define active space based on energy [elw,eup]

elw: lower bound in eV (not in au!).

eup: upper bound in eV.

idiag

  idiag=1: Davidson diagonalization
  idiag=2: full diagonalization
  idiag=3: iVI diagonalization (only Abelian point groups supported)

aokxc

Calculate the XC kernel using the AO direct algorithm. This is the default for AO-TDDFT.

iguess

iguess=10*x+y

  x=0: diagonal guess (default for AO-TDDFT under non-Abelian point groups and MO-TDDFT)
  x=1: read guess from file (when iVI is used, this option only supports C(1) point group)
  x=2: tight-binding guess (default for AO-TDDFT under Abelian point groups, usually much better than the diagonal guess, especially for non-diffuse basis sets). This also invokes a tight-binding preconditioner.
  y=0: do not save eigenvectors during the TD-DFT iterations (default)
  y=1: save eigenvectors at each iteration (when iVI is used, this option only supports C(1) point group)

grimmestd

Requests Grimme's sTDA or sTDDFT method (not to be confused with S-TDDFT, which is a completely unrelated method!), which are approximate TDDFT methods that are much faster (100x or more) than conventional TDDFT, at the cost of introducing an error on the order of 0.2 eV. Note that for transition metal complexes, the error may be considerably larger and may reach 1 eV. When itda=0, the sTDDFT method is used, otherwise the sTDA method is invoked. NOTE: grimmestd cannot be used together with MPEC+COSX. Moreover, TDDFT gradients, dipole moments and NACMEs are not yet supported at the sTDA/sTDDFT level.

Convergence threshold

Note that convergence is signaled if either all roots converged with respect to energy change, OR all roots converged with respect to the norm of residual vectors. Thus, when one wants to tighten the thresholds, it is advised to tighten them both.

crit_e

Threshold for energy change. Default: 1e-7 a.u.

crit_vec

Threshold for the norm of residual vectors. Default: 1e-5.

States specification

iroot,iexit

The number of calculated excited states of each irreducible representation. If there are several irreps for a point group as C2v, iroot states will be calculated for each irreps. Use "iroot" instead of "iexit". "iexit" will be deleted in the future. For example,

# assume H2O molecule with C2v symmetry
$tddft
iroot
 4  # totally 16 roots, 4 roots for A1, A2, B1, B2 irreps
$end

Of course, this can be sometimes wasteful since the roots of some irreps are much higher than the roots of other irreps. It may be desirable to obtain the lowest roots among all irreps, so that if the roots of an irrep are very high-lying, then few or no roots are calculated for this irrep. This kind of calculation can be requested by setting iroot as a negative number:

# assume H2O molecule with C2v symmetry
$tddft
iroot
 -4  # totally 4 roots
$end

In this case the program tries the best to guess the number of roots to be calculated for each irrep. The resulting states are probably the lowest 4 roots among the roots of all the irreps, but this cannot be guaranteed.

nroot, nexit

Same as above, but different numbers can be specified for different irreps. Use nroot instead of nexit. For example:

# assume H2O molecule with C2v symmetry
$tddft
nroot
 2 3 1 4  # irrep A1 - 2 roots; A2 - 3 roots; B1 - 1 root; B2 - 4 roots
$end

iwindow

The excitation energy window in which excited states are to be calculated. If iwindow is specified, the iexit and Nexit keywords (if any) are overridden, so that the actual number of roots calculated are determined by iwindow alone. Two numbers must be provided in the next line, followed by an optional unit (au/eV/nm/cm-1). For example,

  iwindow
  300 700 nm

specifies that all excited states within 300 nm and 700 nm are to be calculated. If no unit is given, the default unit is eV. When the Davidson diagonalization method is used, the calculated excited states are neither guaranteed to include all excited states within the window, nor guaranteed to be all contained in the window. To ensure that all and only those excited states within the window are calculated, the iVI method must be used:

  idiag
  3
  iwindow
  300 700 nm

Note that due to technical reasons, the iVI program requires an upper bound estimate of the number of roots before the calculation. A default value is chosen based on the initial guess, which is usually but not always sufficient; in case it is insufficient, the program will print a warning "too small iroot/nroot, require xxx, but only yyy provided". In this case one should specify Nexit as a number that is at least xxx, and run the calculation again. Under still rarer conditions, the program may abort with the error message "too small ld xxx, require yyy". In this case one should restart the calculation by specifying a maxld parameter that is at least yyy. Thus, the input file may now look like:

  idiag
  3
  nexit
  50
  maxld
  200
  iwindow
  300 700 nm

Save eigenvectors

istore

Integer: specify the file no. to store TDDFT information

lefteig

In TD-DFT, also store the left eigenvector X-Y, in addition to the right eigenvector X+Y. This is turned on by default.

output eigenvector control

nprt

cthrd

TD-DFT/SOC and Property evaluation

nfiles

No. of TD-DFT calculations to be loaded.

isoc

=1, Only work for closed-shell case (NOT recommended!)

=2, General SOC state interaction

=3, just print SOC matrix elements between two spin-free states (without diagonalization Hsoc).

ifgs

=0, default for not including ground state (GS) in SOC treatment; =1, include GS.

imatsoc

Define SOC matrices need to be calculated. Input format looks like

...
#SCF calculation for the ground state S0. It is a singlet.
$scf
spin
 1
...
$end

#First TDDFT, singlets S1-S10.
$tddft
imethod
 1
isf
 0
iexit
 10
....
$end

#Second TDDFT, triplet T1-T10.
$tddft
imethod
 1
isf
 1
iexit
 10
$end

$tddft
....
imatsoc
  8
0 0 0 2 1 1
0 0 0 2 1 2
1 1 1 2 1 1
1 1 1 2 1 2
1 1 2 2 1 1
1 1 2 2 1 2
2 1 1 2 1 1
2 1 1 2 1 2
$end

In this input, 7 means seven of SOC matrices will be calculate (If the number <0, then ALL possible HSOC mat will be printed !). Here, it is very tricky to specify states:

• The string "0 0 0" always stands for the ground state.

• For other states, three numbers "n m n" represent "ith-tddft", "symmetry" and "ithstate" respectively. Therefore, the first matrix element "0 0 0 2 1 1" means SOC matrix of <S0|HSOC|T1>. The third matrix element "1 1 1 2 1 1" means SOC matrix <S1|HSOC|T1>. Here, the first "1" in bra state "1 1 1" means the state from first TDDFT calculation. The second and third "1" in the bra state "1 1 1" means this state has spatial symmetry "1" and is the first excited state.

imatrsf

Transition dipole between Spin-free states. Setting it to -1 prints all of them.

imatrso

Define that the transition dipole moments between which pairs of SOC-included states need to be printed. Input format looks like (notice we omit other input in TDDFT module)

$TDDFT
...
imatrso
5
1 1
1 2
1 3
1 4
1 5
...
$END

Then, "imatrso" is specified to define transition dipole moments need to be printed. The number "5" require transition dipoles between 5-pairs of states to be print. The following 5 lines define which pairs will be printed. Here, we require transition dipoles between the first state and five states are printed.

When the number of spinor states is large, the above syntax may be inconvenient. Therefore we provide two shortcuts. The following input specifies that the transition dipole moments between all pairs of spinor states will be printed:

$TDDFT
...
imatrso
-1
$END

The following input specifies that all ground state-excited state spinor transition dipole moments will be printed:

$TDDFT
...
imatrso
-2
$END

In any case, if a transition dipole moment is requested, the corresponding oscillator strength and radiative transition rate (from Fermi Golden Rule) are printed as well.

imatnso

imatnsf

idiag

By default, idiag=0 uses full diagonalization (preferred for small model space).

If idiag=1, then TD-DFT/SOC can use Davidson's algorithm also, along with a specification for the no. of states by iexit.

iact

=1, allows to use active space specification for the projected active-orbital SOC Hamiltonian (P*HSOC*P), eup can be specified in (eV) to give a cut off to define active physically interested excited states.

ntoanalyze

Natural transition orbital (NTO) analysis. The keyword should be given in a separate TDDFT block, immediately following the TDDFT block that calculated the excited states:

$tddft
nexit
5
$end

$tddft
ntoanalyze
  2      # number of states
  1 3   # list of states in NTO analysis.
$end

The NTOs are written to MOLDEN files, xxx.nto1.molden and xxx.nto3.molden, which correspond to the S1 and S3 excited states, respectively. If one wants to analyze all states computed by the previous TDDFT block, one can write

$tddft
nexit
5
$end

$tddft
ntoanalyze
  0
$end

In this case, the NTOs of all five excited states are obtained.

Stability analysis

The wavefunction stability analysis code is currently under debugging. Instead of a genuine stability analysis, one can instead perform a spin-conserving U-TDDFT calculation. The wavefunction is stable if and only if the lowest excitation energy of the calculation is real and non-negative. However, this is slower than a true stability analysis, and if the wavefunction is unstable, one does not have the option to optimize the wavefunction to a stable one.

isab

isave

memory control

memjkop

specific memory usage for ao-JK calculation (PER THREAD for imemshrink = 0)

imemshrink

imemshrink = 0: default

imemshrink = 1: reduce openmp memory usage for ao-JK and ao-Kxc calculation. Will be slower due to thread lock.

Others

isgn

ivo

Modified Davidson algorithm

Eneshift

Specify an energy window. States with excitation energies close to input value will be calculate. The energy unit is eV.

$TDDFT
Eneshift
 9.0
...
$End

AO-TDDFT and AO-TDA

AO-TDDFT supports R-TDDFT, U-TDDFT, R-TDDFT-SF+1. The possible combinations are
     imethod=1, itda=0, isf=0
     imethod=1, itda=0, isf=1
     imethod=2, itda=0, isf=0
AO-TDA  supports R-TDA,U-TDA, R-TDA-SF+1, R-TDA-SF-1, U-TDA-SF3. The possible combinations are
     imethod=1, itda=1, isf=0
     imethod=1, itda=1, isf=1
     imethod=2, itda=1, isf=0
     imethod=2, itda=1, isf=-1
     imethod=2, itda=1, isf=3

Frozen orbital

Frzorb

Only valid for C1 symmetry.

Frzorb
  4           # number of orbital to be frozen
 1 4 6 7   # orbital list 

Frzcore

Frzcore
 1 2 2 1   # number of core orbitals will be frozen in each irrep

Frzvirt

Frzvirt
 2 2 2 2   # number of virtual orbitals will be frozen in each irrep

Spin-flip Kernel

kernelctrl

=0; (va-vb)*(rhoa-rhob)/( (rhoa-rhob)^2+thrdab)

=2; old version using 2nd order derivatives Only affect GGA spin-flip TDDFT with ALDA0

thrdab

threshold for |rhoa-rhob|

Some uncommon keywords just for testing methods

idrpa

ispa

iro

icv

ioo

iksf