Gaussian 09 Output file_DFT Calcuation

[darwined]

Hi,

I am trying to understand the functional form of B3LYP from the Gaussian output file. I have tried to relate the details in the output file with the functional form of B3LYP. But I am not sure what certain terms correspond to. I have mentioned below the details. Can you pleaese help me.

In the output of TD-DFT calculation files, I see the following (this is an e.g. of B3LYP)

IExCor= 402 DFT=T Ex+Corr=B3LYP ExCW=0 ScaHFX= 0.200000
ScaDFX= 0.800000 0.720000 1.000000 0.810000 ScalE2= 1.000000 1.000000

And in this case, it is well known that the funcitonal B3LYP has 20% Hartree Fock Exchange and 80% Density Exchange, the terms ScaHFX= 0.200000
ScaDFX= 0.800000 which says the scaling factor for HFX is 20% and DFX is 80% respectively. And when summed up, they give the value '1'.

0.720000 corresponds to the coefficient for gradient of Ex(Becke88).

Can someone please tell me what do the last two terms (1.000000 & 0.810000) correspond to.

Please let me know if I am not clear.

 

[TeethWhitener]

From the Gaussian user manual: http://www.gaussian.com/g_tech/g_ur/k_dft.htm

Gaussian 09 can use any model of the general form: P₂E_X^HF + P₁(P₄E_X^Slater + P₃ΔE_x^non-local) + P₆E_C^local + P₅ΔE_C^non-local

...and a little later...

Here is a route section specifying the functional corresponding to the B3LYP keyword:


#P BLYP IOp(3/76=1000002000) IOp(3/77=0720008000) IOp(3/78=0810010000)

The output file displays the values that are in use:


IExCor= 402 DFT=T Ex=B+HF Corr=LYP ExCW=0 ScaHFX= 0.200000
ScaDFX= 0.800000 0.720000 1.000000 0.810000


where the value of ScaHFX is P₂, and the sequence of values given for ScaDFX are P₄, P₃, P₆ and P₅.

 

[darwined]

From the Gaussian user manual: http://www.gaussian.com/g_tech/g_ur/k_dft.htm

Gaussian 09 can use any model of the general form: P₂E_X^HF + P₁(P₄E_X^Slater + P₃ΔE_x^non-local) + P₆E_C^local + P₅ΔE_C^non-local

...and a little later...

Here is a route section specifying the functional corresponding to the B3LYP keyword:#P BLYP IOp(3/76=1000002000) IOp(3/77=0720008000) IOp(3/78=0810010000)

The output file displays the values that are in use:IExCor= 402 DFT=T Ex=B+HF Corr=LYP ExCW=0 ScaHFX= 0.200000
ScaDFX= 0.800000 0.720000 1.000000 0.810000 where the value of ScaHFX is P₂, and the sequence of values given for ScaDFX are P₄, P₃, P₆ and P₅.

Thank you for your response TeethWhitener.

I almost got all the values from Gaussian 09 website (the link that you have provided).

Comparing the information printed in the output file and Gaussian standard format, I can related that P1=1, P2=0.2, P3=0.72, P4=0.8.
But as far as P5 and P6 are concerned, I am not sure what is the value of P5 and P6 are and what is/are the correlation functional(s) used. Is it VWN or LYP or Both.

Can you kindly clarify.

 

[TeethWhitener]

Again from the Gaussian manual:

B3LYP uses the non-local correlation provided by the LYP expression, and VWN functional III for local correlation (not functional V).

So P₅ is LYP and P₆ is VWN functional III.

 

[darwined]

Thank you for the responseTeethWhitener.

Now comparing the Gaussian output file and the coeffecients, can you please tell me if the functional form I have arrived at is correct?

Gaussian output

IExCor= 402 DFT=T Ex+Corr=B3LYP ExCW=0 ScaHFX= 0.200000
ScaDFX= 0.800000 0.720000 1.000000 0.810000 ScalE2= 1.000000 1.000000

Functional form after comparison.

P2*HFX + P1*(P3*DFX + P4*Delta DFX) + P5*LYP + P6*VWN

where P1=1, P2=0.2, P3=0.8, P4=0.72, P6=1 and P5= 0.81.

If it is correct, does this not mean there is 1.81*Ec (P5+P6) in the above equation. Kindly clarify.

 

[TeethWhitener]

Again from the Gaussian manual:

Note that since LYP includes both local and non-local terms, the correlation functional used is actually:

C*E_C^LYP+(1-C)*E_C^VWNIn other words, VWN is used to provide the excess local correlation required, since LYP contains a local term essentially equivalent to VWN.

That should clear everything up. LYP is a special case, because it's got local and nonlocal contributions.

 

[darwined]

Thank you for your swift response. That is exactly where I am confused now. We now have P5 and P6 left. Also from the Gaussian output file , we have 1.000000 0.810000 (the last two terms).

Now according to the manual, if I assign P5(0.81) to be scaling factor for Ec(LYP), I get a question why 0.19 (scaling factor for Ec(VWN)) is not printed in the output. Also then in that case what does P6=1 correspond to?

I am sorry for the trouble caused, but I am feeling very confused in the correlation terms involved.
Please let me know if I am not clear.

Thanks for your help.

 

[TeethWhitener]

Ok let's put it all in one place:

Becke Three Parameter Hybrid Functionals. These functionals have the form devised by Becke in 1993 [http://www.gaussian.com/g_tech/g_ur/refs.htm#Becke93a ]:


A*EXSlater+(1-A)*EXHF+B*ΔEXBecke+ECVWN+C*ΔECnon-local


where A, B, and C are the constants determined by Becke via fitting to the G1 molecule set.
...
There are several variations of this hybrid functional. B3LYP uses the non-local correlation provided by the LYP expression, and VWN functional III for local correlation (not functional V). Note that since LYP includes both local and non-local terms, the correlation functional used is actually:


C*ECLYP+(1-C)*ECVWN


In other words, VWN is used to provide the excess local correlation required, since LYP contains a local term essentially equivalent to VWN.
...
Gaussian 09 can use any model of the general form: P2EXHF + P1(P4EXSlater + P3ΔExnon-local) + P6EClocal + P5ΔECnon-local

...

Here is a route section specifying the functional corresponding to the B3LYP keyword:#P BLYP IOp(3/76=1000002000) IOp(3/77=0720008000) IOp(3/78=0810010000)

The output file displays the values that are in use:IExCor= 402 DFT=T Ex=B+HF Corr=LYP ExCW=0 ScaHFX= 0.200000
ScaDFX= 0.800000 0.720000 1.000000 0.810000 where the value of ScaHFX is P2, and the sequence of values given for ScaDFX are P4, P3, P6 and P5.

So P₄ = A = 0.8, P₂ = 1-A = 0.2, P₃ = B = 0.72, and the correlation functional is E_C^VWN+CΔE_C^non-local. Here E_C^VWN is the local correlation functional, so P₆ = 1. Since LYP has a local and a non-local part, we have to subtract the local fraction from VWN to compensate. So the non-local correlation functional is actually E_C^LYP-E_C^VWN, making P₅ = C = 0.81. But since part of E_C^VWN was already included in P₆, the total amount of E_C^VWN in the final functional ends up being 1-0.81 = 0.19.

 

[darwined]

Dear TeethWhitener,

Sorry for the delay in response.

Thanks for your help throughout. Now things are clear to me.