[Pw_forum] Excited State Gradients in TDDFT

[yukihiro_okuno]

Dear PWSCF users and developers.

I want to know the possibility of excited state gradients in TDDFT
implemented in

Quantum Espresso.

Can the PWSCF calculate the excited state gradients (Force of atoms in
excited state )

by PWSCF, or are there plan to develop the excited state gradient
calculation ?

The implementation of TDDFT in PWSCf uses lanczos method and does not

explicitly calculate the excited energy, and is it difficult to extend to

calculate force in this formalism ?


Sincerely,

Yukihiro Okuno.
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[Stefano Baroni]

Post by yukihiro_okuno
Dear PWSCF users and developers.
I want to know the possibility of excited state gradients in TDDFT implemented in
Quantum Espresso.
Can the PWSCF calculate the excited state gradients (Force of atoms in excited state )

pwscf does not implement any excited-state features (tddft energies, gradient or other). The QE distribution does contain some specialized codes that perform some of these calculations (turbo_tddft implements the Liouville-Lanczos approach to TDDFT, whereas GWL is an implementation of the GW method particularly suitable for large systems)

Post by yukihiro_okuno
by PWSCF, or are there plan to develop the excited state gradient calculation ?
The implementation of TDDFT in PWSCf uses lanczos method and does not
explicitly calculate the excited energy, and is it difficult to extend to
calculate force in this formalism ?

the present implementation of tddft is particularly suited for the calculation of the entire spectrum of large systems, whereas excited-state energy gradients would require the calculation of individual eigenpairs of the Liouvillian. That should not be difficult to implement, but it is not considered to be a priority at this time. Should anybody be interested in implementing this feature, we in Trieste would be delighted to help.

SB

---
Stefano Baroni - SISSA & DEMOCRITOS National Simulation Center - Trieste
http://stefano.baroni.me [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

La morale est une logique de l'action comme la logique est une morale de la pens?e - Jean Piaget

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[yukihiro_okuno]

Dear Prof. Baroni.

Thank you very much for your response.

I'm very glad.

Post by Stefano Baroni

Post by yukihiro_okuno
by PWSCF, or are there plan to develop the excited state gradient

calculation ?

Post by Stefano Baroni

Post by yukihiro_okuno
The implementation of TDDFT in PWSCf uses lanczos method and does not
explicitly calculate the excited energy, and is it difficult to extend to
calculate force in this formalism ?

the present implementation of tddft is particularly suited for the

calculation of the entire spectrum of large systems, whereas excited-state
energy gradients would require the calculation of individual eigenpairs

Post by Stefano Baroni
of the Liouvillian. That should not be difficult to implement, but it is

not considered to be a priority at this time. Should anybody be interested
in implementing this feature, we in Trieste would be delighted to help.

Thank you for your advice.

You mean if we diagonalize the Liouvillean operator by usual method
instead of using Lanczos chain, and get

eigenvalue and eigenvectors, we can get excited-state gradient ?

Are there already formalism to calculate the excited energy gradient
within occupied state only method ?

Usual Casida's matrix, the dimension of the Matrix is \Omega_{i_j, k_q}
where, i and j are occupied and unoccupied state (k and q are also occupied
and unoccupied state pair),

and the dimension is (2*Nc*Nv) * (2* Nc * Nv) where Nc and Nv is the
number of the unoccupied and occupied states.

But your Liouvillean matrix dimension is (2*Nv) * (2 *Nv), and it is very
small than the usual Casida's one.

It seems very attractive to perform the large molecule, because the
possibilities to calculate the large molecule's excited state energy
gradient is very important

quantities in photochemistry.

Sincerely,

Yukihiro Okuno.
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[dario rocca]

Dear Yukihiro

You mean if we diagonalize the Liouvillean operator by usual method
instead of using Lanczos chain, and get
eigenvalue and eigenvectors, we can get excited-state gradient ?

There are not "usual methods" to get eigenvalues and eigenvectors for TDDFT
because the eigenvalue problem is non-Hermitian. I have been lately working
on this type of eigenvalue problems in order to diagonalize the Liouvillian
in the TDDFT formalism without empty states (J. Chem. Phys. 136, 034111
(2012)). This new method seems very promising but at this stage it still
needs an efficient preconditioner to become more practical.

Are there already formalism to calculate the excited energy gradient
within occupied state only method ?

I think that a necessary ingredient for the calculation of gradients is the
diagonalization of the Liouvillian. Once this is done I think that the
formalism used for the Casida's equations can be extended to the TDDFT
without empty states.

Usual Casida's matrix, the dimension of the Matrix is \Omega_{i_j, k_q}
where, i and j are occupied and unoccupied state (k and q are also occupied
and unoccupied state pair),
and the dimension is (2*Nc*Nv) * (2* Nc * Nv) where Nc and Nv is the
number of the unoccupied and occupied states.
But your Liouvillean matrix dimension is (2*Nv) * (2 *Nv), and it is very
small than the usual Casida's one.

The dimension of the Liouvillian is actually (2*Nv*Npw)*(2*Nv*Npw). This
dimension is basically the same as that of Casida's equation when Nc is the
total number of conduction states. The advantage of the Liouvillian
approach is not exactly in the matrix dimension but I would say that some
of the advantages are:
-The matrix is big but never built explicitly and its application to a
vector involve a number of orbitals that is equal to the number of occupied
states (it scales better than Casida's equations, that involve a number of
orbitals equal to Nc)
-The convergence of the spectra with the number of empty states in never an
issue (even at high energy or when there is a strong dependence of the
spectrum at low energy on the states at higher energy)
-The use of plane-waves avoids the convergence problems with respect to the
basis set typical of the localized basis sets

Dario Rocca
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[dario rocca]

Dear Yukihiro

You mean if we diagonalize the Liouvillean operator by usual method
instead of using Lanczos chain, and get
eigenvalue and eigenvectors, we can get excited-state gradient ?

There are not "usual methods" to get eigenvalues and eigenvectors for TDDFT
because the eigenvalue problem is non-Hermitian. I have been lately working
on this type of eigenvalue problems in order to diagonalize the Liouvillian
in the TDDFT formalism without empty states (J. Chem. Phys. 136, 034111
(2012)). This new method seems very promising but at this stage it still
needs an efficient preconditioner to become more practical.

Are there already formalism to calculate the excited energy gradient
within occupied state only method ?

I think that a necessary ingredient for the calculation of gradients is the
diagonalization of the Liouvillian. Once this is done I think that the
formalism used for the Casida's equations can be extended to the TDDFT
without empty states.

Usual Casida's matrix, the dimension of the Matrix is \Omega_{i_j, k_q}
where, i and j are occupied and unoccupied state (k and q are also occupied
and unoccupied state pair),
and the dimension is (2*Nc*Nv) * (2* Nc * Nv) where Nc and Nv is the
number of the unoccupied and occupied states.
But your Liouvillean matrix dimension is (2*Nv) * (2 *Nv), and it is very
small than the usual Casida's one.

The dimension of the Liouvillian is actually (2*Nv*Npw)*(2*Nv*Npw). This
dimension is basically the same as that of Casida's equation when Nc is the
total number of conduction states. The advantage of the Liouvillian
approach is not exactly in the matrix dimension but I would say that some
of the advantages are:
-The matrix is big but never built explicitly and its application to a
vector involve a number of orbitals that is equal to the number of occupied
states (it scales better than Casida's equations, that involve a number of
orbitals equal to Nc)
-The convergence of the spectra with the number of empty states in never an
issue (even at high energy or when there is a strong dependence of the
spectrum at low energy on the states at higher energy)
-The use of plane-waves avoids the convergence problems with respect to the
basis set typical of the localized basis sets

Dario Rocca
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[yukihiro_okuno]

Dear PWSCF users and developers.

I want to know the possibility of excited state gradients in TDDFT
implemented in

Quantum Espresso.

Can the PWSCF calculate the excited state gradients (Force of atoms in
excited state )

by PWSCF, or are there plan to develop the excited state gradient
calculation ?

The implementation of TDDFT in PWSCf uses lanczos method and does not

explicitly calculate the excited energy, and is it difficult to extend to

calculate force in this formalism ?


Sincerely,

Yukihiro Okuno.
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[Stefano Baroni]

Post by yukihiro_okuno
Dear PWSCF users and developers.
I want to know the possibility of excited state gradients in TDDFT implemented in
Quantum Espresso.
Can the PWSCF calculate the excited state gradients (Force of atoms in excited state )

pwscf does not implement any excited-state features (tddft energies, gradient or other). The QE distribution does contain some specialized codes that perform some of these calculations (turbo_tddft implements the Liouville-Lanczos approach to TDDFT, whereas GWL is an implementation of the GW method particularly suitable for large systems)

Post by yukihiro_okuno
by PWSCF, or are there plan to develop the excited state gradient calculation ?
The implementation of TDDFT in PWSCf uses lanczos method and does not
explicitly calculate the excited energy, and is it difficult to extend to
calculate force in this formalism ?

the present implementation of tddft is particularly suited for the calculation of the entire spectrum of large systems, whereas excited-state energy gradients would require the calculation of individual eigenpairs of the Liouvillian. That should not be difficult to implement, but it is not considered to be a priority at this time. Should anybody be interested in implementing this feature, we in Trieste would be delighted to help.

SB

---
Stefano Baroni - SISSA & DEMOCRITOS National Simulation Center - Trieste
http://stefano.baroni.me [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

La morale est une logique de l'action comme la logique est une morale de la pens?e - Jean Piaget

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[yukihiro_okuno]

Dear Prof. Baroni.

Thank you very much for your response.

I'm very glad.

Post by Stefano Baroni

Post by yukihiro_okuno
by PWSCF, or are there plan to develop the excited state gradient

calculation ?

Post by Stefano Baroni

Post by yukihiro_okuno
The implementation of TDDFT in PWSCf uses lanczos method and does not
explicitly calculate the excited energy, and is it difficult to extend to
calculate force in this formalism ?

the present implementation of tddft is particularly suited for the

calculation of the entire spectrum of large systems, whereas excited-state
energy gradients would require the calculation of individual eigenpairs

Post by Stefano Baroni
of the Liouvillian. That should not be difficult to implement, but it is

not considered to be a priority at this time. Should anybody be interested
in implementing this feature, we in Trieste would be delighted to help.

Thank you for your advice.

You mean if we diagonalize the Liouvillean operator by usual method
instead of using Lanczos chain, and get

eigenvalue and eigenvectors, we can get excited-state gradient ?

Are there already formalism to calculate the excited energy gradient
within occupied state only method ?

Usual Casida's matrix, the dimension of the Matrix is \Omega_{i_j, k_q}
where, i and j are occupied and unoccupied state (k and q are also occupied
and unoccupied state pair),

and the dimension is (2*Nc*Nv) * (2* Nc * Nv) where Nc and Nv is the
number of the unoccupied and occupied states.

But your Liouvillean matrix dimension is (2*Nv) * (2 *Nv), and it is very
small than the usual Casida's one.

It seems very attractive to perform the large molecule, because the
possibilities to calculate the large molecule's excited state energy
gradient is very important

quantities in photochemistry.

Sincerely,

Yukihiro Okuno.
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