Tip

All input files can be downloaded: Files.

nosi

This option defines the implementation details of nonothorgonal state interaction (NOSI) calculations for excited and diabaitc states.

offdiag_correlation

Value	`overlap_weighted` Will use overlap weighted method
	`energy_weighted` Will use energy weighted method
	`correlation_potential` Will use correlation functional method, given by the `xc_functional` option
Default	`overlap_weighted`

Define the off-diagonal correlation method.

xc_functional

Value	A valid exchange-correlation functional name
Default	None

When offdiag_correlation is set to correlation_potential, this option is required to specify the exchange-correlation functional to be used. All valid functional names are available in scf.

zero_threshold

Value	A real number
Default	`1.E-6`

When the overlap of two orbitals is smaller than this value, they will be treated as zero

Warning

Do not set a too large value (like 1.E-4). It may leads to wrong results.

files

Value	One or more file names
Default	None

List the mwfn file names of the determinants to be read.

spin_filp

Value

One or more file names

Default

None

List of determinants to perform spin flip (alpha to beta and beta to alpha).

Warning

Only supported when the numbers of alpha electrons and beta electrons number equal.

For example, in the following input:

nosi
    files det1.mwfn det2.mwfn det3.mwfn
    spin_filp  det2.mwfn det3.mwfn
end

In this case, 5 determinants will be used for NOSI calculations:

det1.mwfn
det2.mwfn
det3.mwfn
det2.mwfn (spin flipped)
det3.mwfn (spin flipped)

In this example, we will calculate the ground state and 2 singlet excited states of (E)-Dimethyldiazene with TSO-DFT methods. Then, we will calculate the NOSI for these 3 states. We will use B3LYP/cc-pVTZ level of theory.

Tip

Acutally, in Qbics, the calculation of excited states using TSO+NOSI can be automatically done by a keyword msdft, see msdft for details.

In the following examples, we will calculate the ground and excited states of (E)-Dimethyldiazene using TSO-DFT methods, details of which can be found in TSO-DFT (1): Excited States and scfguess.

dma-s0.inp: Ground state;
dma-s1.inp: S₁ state, corresponding to HOMO (16) → LUMO (17) transition;
dma-s2.inp: S₂ state, corresponding to HOMO-1 (15) → LUMO (17) transition.

dma-s0.inp

basis
    cc-pvtz
end

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

mol
    N     -0.11855722      0.06367877     -0.00010027
    N      1.11855814     -0.06366086     -0.00010026
    C      1.81864333      1.22402113      0.00009549
    H      1.12816980      2.07452976      0.00011126
    H      2.46787129      1.25512096      0.88302715
    H      2.46820089      1.25538193     -0.88260363
    C     -0.81864582     -1.22402070      0.00009559
    H     -0.12816015     -2.07453667      0.00011125
    H     -1.46787530     -1.25512668      0.88303320
    H     -1.46820496     -1.25538766     -0.88260977
end

task
    energy b3lyp
end

dma-s1.inp

basis
    cc-pvtz
end

scf
    charge      0
    spin2p1     1
    type        U
    no_scf      TSO
end

# 16->17
scfguess
    type mwfn
    file dma-s0.mwfn
    orb  32 1  1-15 17-204 : 1-203
    orb   0 1   16 : 204
end

mol
    N     -0.11855722      0.06367877     -0.00010027
    N      1.11855814     -0.06366086     -0.00010026
    C      1.81864333      1.22402113      0.00009549
    H      1.12816980      2.07452976      0.00011126
    H      2.46787129      1.25512096      0.88302715
    H      2.46820089      1.25538193     -0.88260363
    C     -0.81864582     -1.22402070      0.00009559
    H     -0.12816015     -2.07453667      0.00011125
    H     -1.46787530     -1.25512668      0.88303320
    H     -1.46820496     -1.25538766     -0.88260977
end

task
    energy b3lyp
end

dma-s2.inp

basis
    cc-pvtz
end

scf
    charge      0
    spin2p1     1
    type        U
    no_scf      TSO
end

# 15->17
scfguess
    type mwfn
    file dma-s0.mwfn
    orb  32 1  1-14 16-204 : 1-203
    orb   0 1   15 : 204
end

mol
    N     -0.11855722      0.06367877     -0.00010027
    N      1.11855814     -0.06366086     -0.00010026
    C      1.81864333      1.22402113      0.00009549
    H      1.12816980      2.07452976      0.00011126
    H      2.46787129      1.25512096      0.88302715
    H      2.46820089      1.25538193     -0.88260363
    C     -0.81864582     -1.22402070      0.00009559
    H     -0.12816015     -2.07453667      0.00011125
    H     -1.46787530     -1.25512668      0.88303320
    H     -1.46820496     -1.25538766     -0.88260977
end

task
    energy b3lyp
end

After calculation, we can collect the results:

State

Energy (Hartree)

Excited Energy (eV)

S₀

-189.34737058

0

S₁

-189.24112513

2.89

S₂

-189.11479416

6.33

Since TSO-DFT is a single-determinant method, S₁ and S₂ are NOT spin eigenfunctions. To be more accurate, we will use NOSI to get more accurate resutls, using the following 3 input files. They only differ in the offdiag_correlation option.

nosi-1a.inp

basis
    cc-pvtz
end

mol
    N     -0.11855722      0.06367877     -0.00010027
    N      1.11855814     -0.06366086     -0.00010026
    C      1.81864333      1.22402113      0.00009549
    H      1.12816980      2.07452976      0.00011126
    H      2.46787129      1.25512096      0.88302715
    H      2.46820089      1.25538193     -0.88260363
    C     -0.81864582     -1.22402070      0.00009559
    H     -0.12816015     -2.07453667      0.00011125
    H     -1.46787530     -1.25512668      0.88303320
    H     -1.46820496     -1.25538766     -0.88260977
end

nosi
    offdiag_correlation overlap_weighted
    files dma-s0.mwfn dma-s1.mwfn dma-s2.mwfn
    spin_flip dma-s1.mwfn dma-s2.mwfn
end

task
    energy nosi
end

nosi-1b.inp

basis
    cc-pvtz
end

mol
    N     -0.11855722      0.06367877     -0.00010027
    N      1.11855814     -0.06366086     -0.00010026
    C      1.81864333      1.22402113      0.00009549
    H      1.12816980      2.07452976      0.00011126
    H      2.46787129      1.25512096      0.88302715
    H      2.46820089      1.25538193     -0.88260363
    C     -0.81864582     -1.22402070      0.00009559
    H     -0.12816015     -2.07453667      0.00011125
    H     -1.46787530     -1.25512668      0.88303320
    H     -1.46820496     -1.25538766     -0.88260977
end

nosi
    offdiag_correlation energy_weighted
    files dma-s0.mwfn dma-s1.mwfn dma-s2.mwfn
    spin_flip dma-s1.mwfn dma-s2.mwfn
end

task
    energy nosi
end

nosi-1c.inp

basis
    cc-pvtz
end

mol
    N     -0.11855722      0.06367877     -0.00010027
    N      1.11855814     -0.06366086     -0.00010026
    C      1.81864333      1.22402113      0.00009549
    H      1.12816980      2.07452976      0.00011126
    H      2.46787129      1.25512096      0.88302715
    H      2.46820089      1.25538193     -0.88260363
    C     -0.81864582     -1.22402070      0.00009559
    H     -0.12816015     -2.07453667      0.00011125
    H     -1.46787530     -1.25512668      0.88303320
    H     -1.46820496     -1.25538766     -0.88260977
end

nosi
    offdiag_correlation correlation_potential
    xc_functional b3lyp
    files dma-s0.mwfn dma-s1.mwfn dma-s2.mwfn
    spin_flip dma-s1.mwfn dma-s2.mwfn
end

task
    energy nosi
end

You should pay attention to the following points:

The basis sets and molecular structure should be the same as the ones used for TSO-DFT calculations. (You can copy the input files from the TSO-DFT calculations.)
If offdiag_correlation is set to correlation_potential, the xc_functional option should be set as the same as the ones used for TSO-DFT calculations.

In files option, you should list the mwfn file names of the determinants to be read. In spin_flip option, you should list the mwfn file names of the determinants that will be used for spin flip. For example, in the above input, dma-s1.mwfn and dma-s2.mwfn will be used for spin flip. In this case, the NOSI calculation will be performed for the following 5 determinants:

dma-s0.mwfn
dma-s1.mwfn
dma-s1.mwfn (spin flipped)
dma-s2.mwfn
dma-s2.mwfn (spin flipped)

After calculation, we can collect the results. Let’s see nosi-1a.out first:

nosi-1a.out

Read non-orthogonal determinants:
0 dma-s0.mwfn
1 dma-s1.mwfn
Spin flipped: dma-s1.mwfn
2 dma-s2.mwfn
Spin flipped: dma-s2.mwfn
...
---- NOSI Overlap Matrix ----
=============================
                  0              1              2              3              4
   0     1.00000000     0.00000000    -0.00001375     0.00000000     0.00004606
   1     0.00000000     1.00000000     0.00000000     0.00000000    -0.00000000
   2    -0.00001375     0.00000000     1.00000000    -0.00000000     0.00000000
   3     0.00000000     0.00000000    -0.00000000     1.00000000     0.00000000
   4     0.00004606    -0.00000000     0.00000000     0.00000000     1.00000000

---- NO Hamiltonian Matrix Functional ----
==========================================
                  0              1              2              3              4
   0  -189.34737100     0.00000058     0.00260277    -0.00000192    -0.00871858
   1     0.00000058  -189.24112500     0.02084657     0.00000885     0.00001057
   2     0.00260277     0.02084657  -189.24112500     0.00001057     0.00000885
   3    -0.00000192     0.00000885     0.00001057  -189.11479400     0.09206962
   4    -0.00871858     0.00001057     0.00000885     0.09206962  -189.11479400

---- NOSI Coefficients Matrix (column vectors are eigenvectors) ----
====================================================================
                  0              1              2              3              4
   0    -1.00000000     0.00000101    -0.00001030    -0.00001197     0.00003201
   1     0.00000657    -0.70710678    -0.70710678     0.00002152    -0.00006937
   2    -0.00000575     0.70710678    -0.70710678    -0.00002152    -0.00006937
   3    -0.00001417    -0.00002152     0.00006937    -0.70710678    -0.70710678
   4     0.00001496     0.00002152     0.00006937     0.70710678    -0.70710678

---- NOSI Results ----
======================
   State   NOSI Energies  Excited Energy       Osc. Str.        DX        DY        DZ
               (Hartree)            (eV)                    (a.u.)    (a.u.)    (a.u.)
       0   -189.34737100      0.00000000      0.00000000  42.82332   0.00029   0.00187
       1   -189.26197158      2.32371833      0.00000000   0.00003  -0.00001   0.00001
       2   -189.22027843      3.45818894      0.00000000  -0.00001  -0.00008   0.00000
       3   -189.20686368      3.82320418      0.00000000   0.00000   0.00000  -0.00000
       4   -189.02272432      8.83363623      0.93845302   2.85145   0.75310  -0.00001

In Read non-orthogonal determinants:, the determinants are shown:

\(\phi_0\) dma-s0.mwfn
\(\phi_1\) dma-s1.mwfn
\(\phi_2\) dma-s1.mwfn (spin flipped)
\(\phi_3\) dma-s2.mwfn
\(\phi_4\) dma-s2.mwfn (spin flipped)

In NOSI Overlap Matrix, the matrix elements \(\left\langle\phi_i\middle|\phi_j\right\rangle\) are calculated. In NO Hamiltonian Matrix Functional, the matrix elements \(\left\langle\phi_i\left|\hat{H}\right|\phi_j\right\rangle\) are calculated.

In NOSI Coefficients Matrix, the column vectors are eigenvectors of the NOSI Hamiltonian matrix. For example, in column 1, we have:

When a determinant and its spin flipped counterpart are combined with out-of-phases (-0.70710678 and -0.70710678), this is a triplet state. When a determinant and its spin flipped counterpart are combined with in-phases (0.70710678 and 0.70710678), this is a singlet state.

The excited energies are shown in NOSI Results.

Now, we can collect resutls from nosi-1a.out, nosi-1b.out and nosi-1c.out together to get the final results:

State	TSO	Overlap Weighted	Energy Weighted	Correlation Potential
	Excited Energy (eV)	NOSI Excited Energy (eV)	NOSI Excited Energy (eV)	NOSI Excited Energy (eV)
S₀	0	0	0	0
T₁	N/A	2.32	2.32	2.35
S₁	2.89	3.46	3.46	3.43
T₂	N/A	3.82	3.80	5.25
S₂	6.33	8.83	8.85	7.40

We can see that, the NOSI results are generally improved upon TSO results. The results from overlap- and energy-weighted methods are very close to each other, while the results from correlation potential method are slightly different for high-lying states.

For every calculation, a CI coefficient file and a spectrum file are generated. For example, nosi-1a-ci.txt and nosi-1a-spectrum.txt.

Example: Diabatic States of a Transition State 

In opt, we have calculated the transition state of a S_N2 reaction.

In the following examples, we will calculate the diabatic states of Cl-CH₃-Cl using TSO-DFT methods, details of which can be found in TSO-DFT (2): Diabatic States and scfguess.

diab-1.inp: Diabatic state of Cl···CH₃-Cl (reactant complex);
diab-2.inp: Diabatic state of Cl-CH₃···Cl (product complex);

diab-1.inp

basis
    def2-svp
end

scf
    charge     -1
    spin2p1     1
    type        U
    no_scf    tso
end

scfguess
    type fragden
    frag  0 1 1-5
    frag -1 1 6
end

mol
    C     -2.28626983      4.81332375     -0.81110844
    H     -1.77793692      3.91128195     -1.11951067
    H     -1.75817077      5.56455137     -0.24234234
    H     -3.32378354      4.96301934     -1.07305839
   Cl     -1.62247473      5.87896571     -2.80504772
   Cl     -2.93223857      3.76141614      1.19669198
end

task
    energy b3lyp
end

diab-2.inp

basis
    def2-svp
end

scf
    charge     -1
    spin2p1     1
    type        U
    no_scf    tso
end

scfguess
    type fragden
    frag  0 1 1-4 6
    frag -1 1 5
end

mol
    C     -2.28626983      4.81332375     -0.81110844
    H     -1.77793692      3.91128195     -1.11951067
    H     -1.75817077      5.56455137     -0.24234234
    H     -3.32378354      4.96301934     -1.07305839
   Cl     -1.62247473      5.87896571     -2.80504772
   Cl     -2.93223857      3.76141614      1.19669198
end

task
    energy b3lyp
end

After calculation, we will obtain the reactant and product diabatic states: diab-1.mwfn and diab-2.mwfn. Now, using NOSI, we can combine them to obtain 2 adiabatic states:

nosi-2.inp

basis
    def2-svp
end

mol
    C     -2.28626983      4.81332375     -0.81110844
    H     -1.77793692      3.91128195     -1.11951067
    H     -1.75817077      5.56455137     -0.24234234
    H     -3.32378354      4.96301934     -1.07305839
   Cl     -1.62247473      5.87896571     -2.80504772
   Cl     -2.93223857      3.76141614      1.19669198
end

nosi
    files diab-1.mwfn diab-2.mwfn
end

task
    energy nosi
end

In this case, we do not need assign spin_flip option since the reactant and product diabatic states are closed shell. In nosi...end, there is no offdiag_correlation option. This means that the off-diagonal correlation will be calculated using the (default) overlap weighted method.

After calculation, we will obtain the adiabatic states: nosi-2.out:

nosi-2.out

---- NOSI Overlap Matrix ----
=============================
                  0              1
   0     1.00000000     0.76098229
   1     0.76098229     1.00000000

---- NO Hamiltonian Matrix Functional ----
==========================================
                  0              1
   0  -959.99564600  -730.60245583
   1  -730.60245583  -959.99557700

---- NOSI Coefficients Matrix (column vectors are eigenvectors) ----
====================================================================
                  0              1
   0    -0.53311086     1.44624356
   1    -0.53259535    -1.44643349

---- Singlet and Triplet Excitation Energies ----
=================================================
Eigenstate 0: -960.03127186 Hartree; Excitation energy: 0.00000000 eV
Eigenstate 1: -959.73288097 Hartree; Excitation energy: 8.11963379 eV

---- Singlet State Weights ----
===============================
                  0              1
   0     0.50027469     0.49972531
   1     0.49972531     0.50027469

---- NOSI Results ----
======================
   State   NOSI Energies  Excited Energy       Osc. Str.        DX        DY        DZ
               (Hartree)            (eV)                    (a.u.)    (a.u.)    (a.u.)
       0   -960.03127186      0.00000000      0.00000000 -268.39724 567.48539 -94.86319
       1   -959.73288097      8.11921604      1.46991870   1.07003   1.72943  -3.26904

We can see that, unlike the excited states, the diabatic states are highly overlapping (In NOSI Overlap Matrix, \(S_{01} = 0.76098229\)). In NOSI Coefficients Matrix, the column vectors are the adiabatic states, indicating that the reactant and product diabatic states are mixed in a 1:1 ratio in both the ground and excited states.

The adiabatic state energies are shown here (A standard DFT calculation is also given in adiab.inp):

NOSI Adiabatic State 0	NOSI Adiabatic State 1	DFT Adiabatic
-960.03127186 Hartree	-959.73288097 Hartree	-960.05738745 Hartree

nosi

Theoretical Background 

Input Examples 

Example: Excited States of (E)-Dimethyldiazene (Manually)

Example: Diabatic States of a Transition State 

nosi

Theoretical Background

Input Examples

Example: Excited States of (E)-Dimethyldiazene (Manually)

Example: Diabatic States of a Transition State

Theoretical Background 

Input Examples 

Example: Diabatic States of a Transition State 