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. pp-TDA: the Tamm-Dancoff approximation to pp-RPA

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
  isf -1, spin flip down

itda

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

ialda

  ialda=0: full non-collinear kernel (default; recommended for spin-conserving TD-DFT)
  ialda=1: non-collinear ALDA kernel
  ialda=2: non-collinear ALDA0 kernel (recommended for spin-flip TD-DFT)
  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 setted 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: iterative, =2 full diag, =3 iVI diag (TDA and AO-TDDFT supported)

ndiag

aokxc

iguess

iguess=10*x+y

  x=0: diagonal guess (default for MO-TDDFT and AO-TDDFT under Abelian point groups)
  x=1: read guess from file (iVI only, useful for restarting a failed calculation)
  x=2: tight-binding guess (default for AO-TDDFT under Abelian point groups, usually much better than the diagonal guess). 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 (iVI only)

Convergence threshold

crit_e

crit_vec

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

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. 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
  iviop
  1
  iwindow
  300 700 nm

where "iviop 1" specifies that internal roots, rather than external roots, are requested.

Save eigenvectors

istore

Integer: specify the file no. to store TDDFT information

lefteig

By default, in TD-DFT the left eigenvector X-Y is also stored.

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
 0
...
$end

#First TDDFT, singlets S0-S9.
$tddft
imethod
 1
isf
 0
iext
 10
....
$end

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

$tddft
....
imatsoc
  7
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 treat as 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. The input is similar to imatsoc (but currently selected printing is not implemented). Simply use -1 to print all of them.

imatrso

Define transition dipole moment need to be printed between two SOC-included states. 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.

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 analyze.

ntoanalyze
  2      # number of states
  1 3   # list of states in NTO analyze.

Stability analysis

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