I performed the excited state calculations of the singlet state H2 molecule (with a bond length of more than 3.0 angstrom or some other dissociated cases) using the spin-unrestricted TDDFT using the broken-symmetry DFT ground state wavefunction. However, I obtained strange results by using the CAMB3LYP and LC-DFT functionals.
The absolute value of excitation amplitudes for the alpha spin is not in agreement with those for the beta spin. I think, even though I started from the broken-symmetry solution, the absolute value of the alpha and beta excitation amplitudes should be the same with each other because the system is centro-symmetric. The errors occur only when I use the CAM type or LC type functionals.
The following is the sample result using the LC-BLYP functional with the range separating parameter of 0.33 and STO-3G basis set (I modified the source code so that transition multipole moments are not shown. I had created the broken-symmetry initial guess orbital from the Gaussian09 result. So the ground state energy is the same as those by Gaussian09.).
==
Ground state a -0.902159661 a.u.
<S2> = 0.9962
-------------------------------------------------------
Root 1 a 0.363567029 a.u. ( 0.9893166423E+01 eV)
<S2> = 0.0075
-------------------------------------------------------
Transition Moments X 0.0000000000E+00 Y 0.0000000000E+00 Z -0.3757053053E-02
Oscillator Strength 0.00000
Occ. 1 alpha a --- Virt. 2 alpha a 0.71783 X
Occ. 1 alpha a --- Virt. 2 alpha a 0.00113 Y
Occ. 1 beta a --- Virt. 2 beta a 0.69622 X
Occ. 1 beta a --- Virt. 2 beta a 0.00110 Y
-------------------------------------------------------
Root 2 a 0.365666203 a.u. ( 0.9950287885E+01 eV)
<S2> = 0.0000
-------------------------------------------------------
Transition Moments X 0.0000000000E+00 Y 0.0000000000E+00 Z -0.2451802116E+00
Oscillator Strength 0.01465
Occ. 1 alpha a --- Virt. 2 alpha a 0.69622 X
Occ. 1 alpha a --- Virt. 2 alpha a -0.00090 Y
Occ. 1 beta a --- Virt. 2 beta a -0.71783 X
Occ. 1 beta a --- Virt. 2 beta a 0.00093 Y
==
Additionally, the excitation energies, transition moments and S^2 values of the excited states did not agree with those calculated by the Gaussian09, although I set the same parameters for CAM and LC, and I obtained the same results for the ground state properties.
The bug is specific for the CAM or LC functional. Additionally, I obtained fairly the same absolute values of the excitation amplitudes for alpha and beta spins using the other functionals, such as, BLYP, B3LYP, etc. The following is the sample result using the BLYP functional.
==
Ground state a -0.926077026 a.u.
<S2> = 0.9946
-------------------------------------------------------
Root 1 a 0.258864235 a.u. ( 0.7044057234E+01 eV)
<S2> = 0.0107
-------------------------------------------------------
Transition Moments X 0.0000000000E+00 Y 0.0000000000E+00 Z -0.3997518983E-10
Oscillator Strength 0.00000
Occ. 1 alpha a --- Virt. 2 alpha a 0.70750 X
Occ. 1 alpha a --- Virt. 2 alpha a 0.02370 Y
Occ. 1 beta a --- Virt. 2 beta a 0.70750 X
Occ. 1 beta a --- Virt. 2 beta a 0.02370 Y
-------------------------------------------------------
Root 2 a 0.262033836 a.u. ( 0.7130306495E+01 eV)
<S2> = 0.0000
-------------------------------------------------------
Transition Moments X 0.0000000000E+00 Y 0.0000000000E+00 Z -0.3016474496E+00
Oscillator Strength 0.01590
Occ. 1 alpha a --- Virt. 2 alpha a 0.70737 X
Occ. 1 alpha a --- Virt. 2 alpha a 0.01940 Y
Occ. 1 beta a --- Virt. 2 beta a -0.70737 X
Occ. 1 beta a --- Virt. 2 beta a -0.01940 Y
==
The bug is also specific for the spin-unrestricted broken-symmetry TDDFT. I did not face a bug when I used the spin-restricted TDDFT. The NWChem-6.0 and Gaussian09 results coincided with each other in such case.
Regards,
RK
|