This is an important point in studies of absorption spectra where many different
types of transitions are present.
In CV-DFT we use approximate ground state functionals in a variational
description of the excited states. Such a procedure is consistent with AD-TDDFT
in that this theory is equivalent to CV(2)-DFT within the TD-approximation. Going
beyond the adiabatic approximation by introducing frequency-dependent kernels
consistent with the approximate ground state functional in TDDFT has proven
difficult. Here we go beyond CV(2)-DFT in a variational approach, still using an
approximate ground state functional but introducing an optimization of U based on
the KS-energy to all orders in U as well as relaxation of the inactive orbitals. It is
hoped that going beyond CV(2) in this way is equivalent to introducing a
frequency-dependent kernel in TDDFT. Obviously with such a kernel, inactive
orbitals would be different from those of the ground state and vary between excited
states as in the RSCF-CV(1) scheme. Further, with a frequency-dependent kernel
and related Hessian, the U matrix obtained for each excited state should be different
from that determined by the ground state Hessian in AD-TDDFT, just as in the
SCF-CV(1)-DFT scheme. At present, CV-DFT has the same problems as TDDFT
with regards to bond dissociation. Work is under way to introduce doubles into the
description of one-electron transitions [99, 100]. This should ensure a prober bond
dissociation and provides for a better description of the electron spectra of polyenes
[36]. The perturbative P-CV(1)-DFT approach doubles the time required for each
excitation compared to TDDFT, whereas the increase is fivefold for RSCF-CV(1).
This might change with more efficient iterative procedures.
Acknowledgement T.Z. would like to thank the Canadian government for a Canada research
chair in theoretical inorganic chemistry and NSERC for financial support.
References
1. Jensen F (2006) Introduction to computational chemistry. Wiley, New York
2. Helgaker T, Jørgensen P, Olsen J (2000) Molecular electronic-structure theory. Wiley,
New York
3. Runge E, Gross EKU (1984) Density functional theory for time-dependent systems. Phys Rev
Lett 52:997
4. Casida ME (1995) In: Chong DP (ed) Recent advances in density functional methods. World
Scientific, Singapore, pp 155–193
5. van Gisbergen SJA, Snijders JG (1995) A density functional theory study of frequency
dependent polarizabilities and Van der Waals dispersion coefficients for polyatomic molecules. J Chem Phys 103:9347
6. Petersilka M, Grossmann UJ, Gross EKU (1996) Excitation energies from time-dependent
density-functional theory. Phys Rev Lett 76:12
7. Bauernschmitt R, Ahlrichs R (1996) Treatment of electronic excitations within the adiabatic
approximation of time dependent density functional theory. Chem Phys Lett 256:454
8. Furche F (2001) On the density matrix based approach to time-dependent density functional
response theory. J Chem Phys 114:5882
Constricted Variational Density Functional Theory Approach to the. . .
91
types of transitions are present.
In CV-DFT we use approximate ground state functionals in a variational
description of the excited states. Such a procedure is consistent with AD-TDDFT
in that this theory is equivalent to CV(2)-DFT within the TD-approximation. Going
beyond the adiabatic approximation by introducing frequency-dependent kernels
consistent with the approximate ground state functional in TDDFT has proven
difficult. Here we go beyond CV(2)-DFT in a variational approach, still using an
approximate ground state functional but introducing an optimization of U based on
the KS-energy to all orders in U as well as relaxation of the inactive orbitals. It is
hoped that going beyond CV(2) in this way is equivalent to introducing a
frequency-dependent kernel in TDDFT. Obviously with such a kernel, inactive
orbitals would be different from those of the ground state and vary between excited
states as in the RSCF-CV(1) scheme. Further, with a frequency-dependent kernel
and related Hessian, the U matrix obtained for each excited state should be different
from that determined by the ground state Hessian in AD-TDDFT, just as in the
SCF-CV(1)-DFT scheme. At present, CV-DFT has the same problems as TDDFT
with regards to bond dissociation. Work is under way to introduce doubles into the
description of one-electron transitions [99, 100]. This should ensure a prober bond
dissociation and provides for a better description of the electron spectra of polyenes
[36]. The perturbative P-CV(1)-DFT approach doubles the time required for each
excitation compared to TDDFT, whereas the increase is fivefold for RSCF-CV(1).
This might change with more efficient iterative procedures.
Acknowledgement T.Z. would like to thank the Canadian government for a Canada research
chair in theoretical inorganic chemistry and NSERC for financial support.
References
1. Jensen F (2006) Introduction to computational chemistry. Wiley, New York
2. Helgaker T, Jørgensen P, Olsen J (2000) Molecular electronic-structure theory. Wiley,
New York
3. Runge E, Gross EKU (1984) Density functional theory for time-dependent systems. Phys Rev
Lett 52:997
4. Casida ME (1995) In: Chong DP (ed) Recent advances in density functional methods. World
Scientific, Singapore, pp 155–193
5. van Gisbergen SJA, Snijders JG (1995) A density functional theory study of frequency
dependent polarizabilities and Van der Waals dispersion coefficients for polyatomic molecules. J Chem Phys 103:9347
6. Petersilka M, Grossmann UJ, Gross EKU (1996) Excitation energies from time-dependent
density-functional theory. Phys Rev Lett 76:12
7. Bauernschmitt R, Ahlrichs R (1996) Treatment of electronic excitations within the adiabatic
approximation of time dependent density functional theory. Chem Phys Lett 256:454
8. Furche F (2001) On the density matrix based approach to time-dependent density functional
response theory. J Chem Phys 114:5882
Constricted Variational Density Functional Theory Approach to the. . .
91