I am running TDSCF calculations using the DFT method and many times for some transitions the coefficient is negative. Could you please explain to me what is the meaning of this?
What coefficients? Those in front of excited Slater determinants? If yes, then it is nothing wrong with that, since the wave function of an excited state is just a linear combination of determinants.
Hello and thank you very much for your response. Below is what the output for the TDSCF looks like. I m referring to the number next to each transition.
i.e. in excited state 2 I have to transitions with105 --> 107 having positive coeficient and the 106--> 108 having negative coefficient. For excited state 3 the coeeficients are both positive. I learned that if I get the square of this coefficient multiple by 2 and then by 100 the resulting number is the percentage contribution of that transition to the resulting excited state. But is there any physical meaning behind the negative numbers?
Excited State 1: Singlet-A 2.2296 eV 556.07 nm f=1.6974
106 ->107 0.59575
This state for optimization and/or second-order correction.
Copying the excited state density for this state as the 1-particle RhoCI density.
Excited State 2: Singlet-A 2.7489 eV 451.04 nm f=0.0000
105 ->107 0.60121
106 ->108 -0.34754
Excited State 3: Singlet-A 3.4044 eV 364.19 nm f=0.0000
105 ->107 0.25382
106 ->108 0.55679
Excited State 4: Singlet-A 3.4421 eV 360.20 nm f=0.0578
98 ->107 -0.11694
104 ->107 0.63156
105 ->108 -0.18425
106 ->111 0.13573
Excited State 5: Singlet-A 3.4656 eV 357.76 nm f=0.0008
100 ->108 0.14517
102 ->107 0.67156
Excited State 6: Singlet-A 3.4917 eV 355.08 nm f=0.0000
100 ->107 0.67247
102 ->108 0.15154
In case of CIS the N-electron wave function is constructed as a linear combination of singly-excited Slater determinants (i.e. one column in such determinant is exchanged by a virtual spinorbital). Optimized CIS coefficients can be positive or negative. Psi_1=c*Phi1+c*Phi2 and Psi_2=c*Phi1-c*Phi2 are two different electronic states (here Phi1 and Phi2 are some example Slater singly-excited determinants). Similarly, from 1sA and 1sB atomic orbitals of H2+ we get one bonding and one antibonding orbital. You don't say that sigma=1sA+1sB and sigma*=1sA-1sB are the same, do you?
You can also see that some quantities, like transition densities and one-electron densities depend on sign of coefficients, look e.g. at the corresponding formulas for CIS in the paper: Foresman at el., J. Phys.Chem, 1992, 96, 135-149, eqs. 2.25, 2.26 etc.
f=1.6974
I'm wondering if an oscillator strength above 1.0 relates to "good physics"; I thought it should be 0
@Stephan Steinmann
Look at this link (it is a blog of Felix Plasser) for the answer:
http://chemical-quantum-images.blogspot.com/2013/12/oscillator-strengths.html
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