Tip

All input files can be downloaded: Files.

Tip

Please refer to scf for more examples.

For a complete tutorial of TSO-DFT, please refer to:

• TSO-DFT (1): Excited States

• TSO-DFT (2): Diabatic States

scfguess

This option defines the initial guess of SCF calculations.

Options

type

Value	hcore Will use the eigenvectors of the core matrix as initial guess. Usually, its performance is very bad
	atmden Will use the superposition of converged densities of all atoms in the system as initial guess. It is recommended for most cases
	fragden Will use the superposition of converged densities of fragments assigned by you as initial guess. This can be used for TSO or treating symmetry-broken systems
	mwfn Will read a wave function from a MWFN file as initial guess
	tso Will use a reference state (assigned with frag) to perform TSO calculation (assigned with orb). This is only used for TSO calculations
Default	atmden

Define the type of initial guess. In most cases, atmden is recommended. mwfn which reads a guess from a converged SCF is also a good choice.

For target state optimization (TSO), symmetry-broken, or other special calculations, fragden can be used.

file

Value	A file name
Default	job name + .mwfn

When type is mwfn, Qbics will read wave function with using mwfn file name.

When type is tso, Qbics will save reference wave function using this mwfn file name.

frag

This defines atomic fragments for initial guess. The format is:

frag num_electrons spin_multiplicity atom_range

There can be arbitrary number of fragments, but all atoms must be included once and only once. They are only activated when type is fragden or tso.

For example:

scfguess
   type fragden
   frag 0 1 1-9
   frag 0 -3 10-15 18
   frag -1 3 16 17
end

In this case, the molecule is decomposed into 3 fragments: (1) atom 1,2,3,4,5,6,7,8,9, with charge 0 and spin multiplicity 1; (2) atom 10,11,12,13,14,15,18, with charge 0 and spin multiplicity 3 (beta orbitals occupied first); (3) atom 16,17, with charge -1 and spin multiplicity 3.

For this guess, Qbics will perform 3 SCF calculations for all fragments, then superpose them as the initial guess for the SCF of the whole molecule. This can be used for ordinary, symmetry-broken, or TSO SCF.

Hint

The total charge of fragments does not have to be the same as the total system.

Hint

Please refer to the keyword no_scf in scf for more details about TSO, when you want to use frag.

orb

This defines the orbitals for initial guess. The format is:

orb num_electrons spin_multiplicity  alpha_MO_indices : beta_MO_indices

There can be arbitrary number of orbital spaces, but all orbitals must be included once and only once. They are only activated when type is mwfn or tso.

For example:

scfguess
   type mwfn
   file x.mwfn
   orb 12 1 1-6 : 1-6
   orb 2 1 7 : 8
   orb 0 1 8 : 7
end

In this case, the orbitals will be read from x.mwfn and 3 orbital spaces are defined: (1) alpha orbital 1,2,3,4,5,6 and beta orbital 1,2,3,4,5,6, with 12 electron and spin multiplicity 1; (2) alpha orbital 7 and beta orbital 8, with 2 electrons and spin multiplicity 1; (3) alpha orbital 8 and beta orbital 7 with 0 electron and spin multiplicity 1 (since no electrons in this orbital space, actually spin multiplicity can be arbitrary).

For this guess, Qbics will read orbitals from x.mwfn and assign occupation according to orb, then do the following ordinary or TSO SCF calculations.

Also, note that in this keyword, orbital order matters. For example,

scfguess
   type mwfn
   file x.mwfn
   orb 14 1 1-6 9 7 8 10-25 : 1-6 9 7 8 10-25
end

In this case, the 7 alpha and 7 beta electrons will occupy orbital 1,2,3,4,5,6,9.

Hint

Please refer to the keyword no_scf in scf for more details about TSO, when you want to use orb.

ble

This defines orbital occupations for a specific excited-state configuration. The format is:

ble block_index alpha_occ_indices : beta_occ_indices

• block_index must be less than the number of blocks (i.e., the number of orb commands used to define orbital blocks).

• The ble keyword is only activated when type is set to mwfn or tso.

For example,

scfguess
    type mwfn
    file x.mwfn
    orb 12 1 1-6 : 1-6
    orb 2 1 7-8 : 7-8
    ble 2 1 : 2
end

In this example:

• Orbitals are read from x.mwfn.

• Two orbital blocks are defined.

• The ble keyword specifies the excitation configuration:

  • In block 2: alpha orbital 7 is occupied, and beta orbital 8 is occupied.

  • These correspond to occupation numbers 1 and 2, respectively.

If the ble keyword is not used, occupations will be assigned according to the orb specification. If ble is used, occupations are overridden and assigned based on ble.

Hint

Please refer to the keyword no_scf in scf for more details about BLE.

Theoretical Background

XXXXXXX

Input Examples

Example: Using Initial Guess of Neutral Dieldrin for Cationic Dieldrin

In scf, we have shown hown to do SCF calculations for Dieldrin. For cationic dieldrin, the SCF took 24 cycles to converge. However, if we use the initial guess from the converged neutral dieldrin, the SCF will converge faster. To do this, we can use the following input:

scfguess-1.inp

basis
    def2-svp
end

scf
    charge  +1
    spin2p1  2
end

scfguess
    type mwfn
    file scf-1a.mwfn
end

grimmedisp
    type bj
end

mol
    Cl    1.40900    -0.54900    -0.14200
    C    2.91800    0.22200    -0.14800
    C    3.34900    1.18000    -0.99000
    Cl    2.48900    1.91800    -2.24800
    C    4.73000    1.60600    -0.53700
    Cl    5.24600    3.22500    -0.97500
    C    5.80600    0.51900    -0.74700
    C    6.83600    -0.13400    -1.70000
    C    6.40300    -1.62200    -1.82900
    C    6.19900    -1.81300    -0.26300
    C    7.62200    -1.50500    0.16600
    O    8.02000    -0.22000    0.59300
    C    8.09500    -0.42900    -0.82100
    C    5.11900    -0.73000    -0.15200
    C    4.07300    -0.11600    0.82100
    Cl    3.68500    -1.10500    2.20000
    C    4.50000    1.37200    1.05000
    Cl    5.90100    1.54700    2.17100
    Cl    3.22100    2.43400    1.80000
    H    6.52400    1.00200    -0.09500
    H    7.05500    0.38900    -2.63100
    H    7.19900    -2.27000    -2.21800
    H    5.50600    -1.77200    -2.43800
    H    5.86900    -2.82100    -0.00200
    H    8.25600    -2.36000    0.34800
    H    9.03900    -0.55400    -1.32700
    H    4.42500    -1.17200    -0.89200
end

task
    energy b3lyp
end

Here, in scfguess...end option, we set the initial guess type to mwfn and read the wave function from scf-1a.mwfn file, which is the converged neutral dieldrin. In scfguess-1.out, you can see that the SCF will converge in 12 cycles, which is much faster than the 24 cycles without this initial guess.

Example: Superposition of Fragment Density for [CH₃NH₄⁺][HSO₄^-]

Now we want to calculate the energy of a cantion-anion pair [CH₃NH₄⁺][HSO₄^-]. The total charge of the system is 0, so the input file can be given in scfguess-2a.inp. However, chemical intuition tells us that an initial guess of superposition of CH₃NH₄⁺ and HSO₄^- seems to be better. This can be given in scfguess-2b.inp:

scfguess-2a.inpscfguess-2b.inp

scfguess-2a.inp

basis
    def2-svp
end

scf
    charge  0
    spin2p1 1
end

mol
 S                 -0.92132000    0.13553700    0.02022300
 O                 -1.71190900    1.32700700    0.03005900
 O                 -1.95455400   -1.09662200   -0.01287200
 O                 -0.09369700   -0.02457400   -1.18931900
 O                 -0.13508200   -0.13905500    1.21845100
 N                  2.13478700   -0.64814300   -0.03200000
 C                  3.06391300    0.49644100    0.01002200
 H                 -2.74409400   -0.79280600   -0.47259900
 H                  1.37775700   -0.50028000   -0.76845000
 H                  1.50266300   -0.65123600    0.79672500
 H                  3.62254900    0.54819100   -0.92118700
 H                  3.74619000    0.39302500    0.85034900
 H                  2.46986400    1.39919200    0.12858400
 H                  2.60115300   -1.54036700   -0.14368500
end

task
    energy b3lyp
end

In scfguess-2b.inp, the fragment initial guess is set using

scfguess-2b.inp

scfguess
    type fragden
    frag -1 1  1-5 8
    frag +1 1  6 7 9-14
end

Here, the atomic indices of CH₃NH₄⁺ and HSO₄^- are given in 1-5 8 and 6 7 9-14, respectively, and charges and spin multiplicities are also given. The atomic indices are shown below:

In their output scfguess-2a.out and scfguess-2b.out, both give the same energy, but the SCF cycles are 25 and 11, respectively. Thus, superposition of fragments is indeed a better initial guess.

Also, we can check the Mulliken population of this system:

scfguess-2b.out

Mulliken Populations
====================
     #  Symbol          Charge            Spin
----------------------------------------------
     1       S      1.06432061      0.00000000
     2       O     -0.48154427      0.00000000
     3       O     -0.35593323      0.00000000
     4       O     -0.56975508      0.00000000
     5       O     -0.56231274      0.00000000
     6       N     -0.03632083      0.00000000
     7       C      0.05819466      0.00000000
     8       H      0.18495781      0.00000000
     9       H      0.18311761      0.00000000
    10       H      0.17532487      0.00000000
    11       H      0.05607280      0.00000000
    12       H      0.05428454      0.00000000
    13       H      0.07504981      0.00000000
    14       H      0.15454343      0.00000000
----------------------------------------------
   Sum             -0.00000000      0.00000000
----------------------------------------------

We can see that, the sum of Mulliken charge on CH₃NH₄⁺ and HSO₄^- are +0.72 and -0.72, respectively, being quite different from their ideal value +1 and -1. This is actually the electron delocalization effect.

Example: Diatatic State of [CH₃NH₄⁺][HSO₄^-] with TSO-DFT

Tip

For a complete tutorial of TSO-DFT, please refer to:

• TSO-DFT (1): Excited States

• TSO-DFT (2): Diabatic States

In the last example, we have calculated [CH₃NH₄⁺][HSO₄^-], where electron is delocalzied over the entire cluster. Can we calculate a state where all electrons are strictly localzied on each molecule? This can be done easily with Qbics. Such state can be called a diabatic state. Diabatic state can be calculated with TSO-DFT method, which can be done with scfguess-3.inp:

scfguess-3.inp

basis
    def2-svp
end

scf
    charge  0
    spin2p1 1
    no_scf  tso
    type    U # This must be given for TSO calculation.
end

scfguess
    type fragden
    frag -1 1  1-5 8
    frag +1 1  6 7 9-14
end

mol
 S                 -0.92132000    0.13553700    0.02022300
 O                 -1.71190900    1.32700700    0.03005900
 O                 -1.95455400   -1.09662200   -0.01287200
 O                 -0.09369700   -0.02457400   -1.18931900
 O                 -0.13508200   -0.13905500    1.21845100
 N                  2.13478700   -0.64814300   -0.03200000
 C                  3.06391300    0.49644100    0.01002200
 H                 -2.74409400   -0.79280600   -0.47259900
 H                  1.37775700   -0.50028000   -0.76845000
 H                  1.50266300   -0.65123600    0.79672500
 H                  3.62254900    0.54819100   -0.92118700
 H                  3.74619000    0.39302500    0.85034900
 H                  2.46986400    1.39919200    0.12858400
 H                  2.60115300   -1.54036700   -0.14368500
end

task
    energy b3lyp
end

We just need to add no_scf tso to scf...end, and give fragment definition in scfguess...end. Also, you must explicitly write type U to enforce unrestricted SCF. Such method can be called TSO-B3LYP. In the output scfguess-3.out:

scfguess-3.out

Mulliken Populations
====================
     #  Symbol          Charge            Spin
----------------------------------------------
     1       S      1.05819195     -0.00000000
     2       O     -0.49810728      0.00000000
     3       O     -0.36249350     -0.00000000
     4       O     -0.71399133      0.00000000
     5       O     -0.66324621     -0.00000000
     6       N     -0.09172438     -0.00000000
     7       C      0.05015632      0.00000000
     8       H      0.17964637      0.00000000
     9       H      0.35411645      0.00000000
    10       H      0.29719708      0.00000000
    11       H      0.06307774     -0.00000000
    12       H      0.06123412     -0.00000000
    13       H      0.09862277     -0.00000000
    14       H      0.16731989      0.00000000
----------------------------------------------
   Sum             -0.00000000     -0.00000000
----------------------------------------------
..omitted..
Final total energy:        -795.63743617 Hartree

We can see that, the sum of Mulliken charge on CH₃NH₄⁺ and HSO₄^- are +1 and -1. So we have successfully obtained the diabatic state we need. Also, its energy -795.63743617 Hartree is higher than the one obatained from scfguess-2b.out: -795.67538949 Hartree. Their difference

-795.67538949 Hartree--795.63743617 Hartree = 23.82 kcal/mol

is actually the Charge transfer interaction energy without BSSE correction defined in TSO-EDA, which can be calculated with eda. The following input:

scfguess-3eda.inp

basis
    def2-svp
end

scf
    charge  0
    spin2p1 1
    type    U # This must be given.
end

eda
    type tso
    frag -1 1  1-5 8
    frag +1 1  6 7 9-14
end

mol
 S                 -0.92132000    0.13553700    0.02022300
 O                 -1.71190900    1.32700700    0.03005900
 O                 -1.95455400   -1.09662200   -0.01287200
 O                 -0.09369700   -0.02457400   -1.18931900
 O                 -0.13508200   -0.13905500    1.21845100
 N                  2.13478700   -0.64814300   -0.03200000
 C                  3.06391300    0.49644100    0.01002200
 H                 -2.74409400   -0.79280600   -0.47259900
 H                  1.37775700   -0.50028000   -0.76845000
 H                  1.50266300   -0.65123600    0.79672500
 H                  3.62254900    0.54819100   -0.92118700
 H                  3.74619000    0.39302500    0.85034900
 H                  2.46986400    1.39919200    0.12858400
 H                  2.60115300   -1.54036700   -0.14368500
end

task
    eda b3lyp
end

At the end of the output scfguess-3eda.out:

scfguess-3eda.out

Target State Optimized Wavefunction Energy Decomposition Analysis
=================================================================
WITHOUT BSSE correction:
Electrostatic interaction energy:                -129.90 kcal/mol
Exchange-correlation interaction energy:           35.20 kcal/mol
Polarization interaction energy:                  -13.18 kcal/mol
Charge transfer interaction energy:               -23.82 kcal/mol
Grimme's dispersion interaction:                    0.00 kcal/mol
----------------------------------------------------------------
Total interaction energy:                        -131.69 kcal/mol

WITH BSSE correction:
Electrostatic interaction energy:                -129.90 kcal/mol
Exchange-correlation interaction energy:           35.20 kcal/mol
Polarization interaction energy:                  -13.18 kcal/mol
Charge transfer interaction energy:               -16.31 kcal/mol
Grimme's dispersion interaction:                    0.00 kcal/mol
----------------------------------------------------------------
Total interaction energy:                        -124.18 kcal/mol

Line 7 says Charge transfer interaction energy:               -23.82 kcal/mol, which is exactly the same value as we calculated.

Example: TSO-DFT for Doubly Excited States of HCHO

Tip

For a complete tutorial of TSO-DFT, please refer to:

• TSO-DFT (1): Excited States

• TSO-DFT (2): Diabatic States

As mentioned above, TSO-DFT can be used to study diabatic states. It can also be used to study excited states. Here, we demonstrate how to use TSO-DFT to calculate a doubly excitated state of HCHO. We consider HOMO² → LUMO²:

scfguess-4a.inp

basis
    element
    H cc-pVTZ
    C cc-pCVTZ
    O cc-pCVTZ
end

scf
    charge      0
    spin2p1     1
    type        U # For TSO-DFT, unrestricted SCF is preferred.
    no_scf      TSO
end

scfguess
    type tso
    file hcho-ref.mwfn
    frag 0 1 1-4
    orb 16 1 1-7 9-114 : 1-7 9-114
    orb  0 1 8 : 8
end

mol
    C -0.000756 -0.520733 0.
    H  0.935697 -1.111766 0.
    H -0.939631 -1.107897 0.
    O  0.001792  0.678123 0
end

task
    energy b3lyp
end

Here:

• Line 16: Set type to tso enable special initial guess for TSO-DFT;

• Line 17: The reference wavefunction (ground state of HCHO) is saved to hcho-ref.mwfn;

• Line 18: Define the reference state. Here, the whole molecule is treated as the reference state;

• Line 19,20: Define the orbital spaces to set up the required excited state as explained above.

After calculation, you can find these lines in scfguess-4a.out:

scfguess-4a.out

TSO Transition
==============
Reference wave function read from: hcho-ref.mwfn
Reference energy:         -114.55175800 Hartree
Current energy:           -114.15907196 Hartree
E(Current)-E(Ref):          10.68553145 eV
Transition dipole moment (Debye):   0.00000   0.00000   0.00000
Oscillator strength:                0.00000
Higher order corrections:
Transition quadrupole moment (Debye*Angstrom):
 Qxx:   0.00000; Qyy:   0.00000; Qzz:   0.00000
 Qxy:   0.00000; Qxz:   0.00000; Qyz:   0.00000
Quadrupole correction to oscillator strength: 0.00000E+00
Transition angular momentum (au):   0.00000   0.00000   0.00000
Magnetic dipole correction to oscillator strength: 0.00000E+00

 ---- Self Consistent Field Energy Done ------------------

Final total energy:        -114.15907196 Hartree

The double excitation energy is 10.68 eV, which agrees well with the one obtained from EOM-CC (10.34 eV). Note that, by changing energy in scfguess-4a.inp to opt, you can do geometry optimization for this excited state!

You can also use an MWFN file as the initial guess to do TSO-DFT calculation:

scfguess-4b.inp

basis
    element
    H cc-pVTZ
    C cc-pCVTZ
    O cc-pCVTZ
end

scf
    charge      0
    spin2p1     1
    type        U # For TSO-DFT, unrestricted SCF is preferred.
    no_scf      TSO
end

scfguess
    type mwfn
    file hcho-ref.mwfn
    orb 16 1 1-7 9-114 : 1-7 9-114
    orb  0 1 8 : 8
end

mol
    C -0.000756 -0.520733 0.
    H  0.935697 -1.111766 0.
    H -0.939631 -1.107897 0.
    O  0.001792  0.678123 0
end

task
    energy b3lyp
end

Note that we have deleted frag 0 1 1-4 since reference wavefucntion is already given in hcho-ref.mwfn. The obtained energy in scfguess-4b.out is exactly the same as in scfguess-4a.out.