## Diborane Jastrow optimization

General discussion of the Cambridge quantum Monte Carlo code CASINO; how to install and setup; how to use it; what it does; applications.
Posts: 138
Joined: Wed Apr 15, 2015 3:14 pm

### Diborane Jastrow optimization

I find out that diborane molecule https://en.wikipedia.org/wiki/Diborane is very hard system to optimize JASTROW and get precise DMC energy result.
Conventional geometry is:

Code: Select all

``````0 1
B        -1.660868686000      0.000000000000      0.000000000000
B         1.660868686000      0.000000000000      0.000000000000
H         0.000000000000      0.000000000000      1.842901487000
H         0.000000000000      0.000000000000     -1.842901487000
H        -2.744534842000      1.964670992000      0.000000000000
H        -2.744534842000     -1.964670992000      0.000000000000
H         2.744534842000     -1.964670992000      0.000000000000
H         2.744534842000      1.964670992000      0.000000000000
``````
Pure madmin JASTROW optimization is very unstable as long as we do not exclude hydrogen atoms from e-e-n term.
After emin optimization DMC gave very/enormously large N_corr value.
For the dtdmc = 0.00667 = 1/(6*Z^2) au, N_corr is 71.69 +/- 14.66.

dtdmc * N_corr = 0.48 au

initial JASTROW in casl format is:

Code: Select all

``````JASTROW:
TERM 1:
Rank:
2
0
Rules:
1-1=2-2
e-e basis:
Type: natural power
Order: 8
e-e cusp: T
e-e cutoff:
Type: alt polynomial
TERM 2:
Rank:
1
1
Rules:
n3=n4
n3=n5
n3=n6
n3=n7
n3=n8
n1=n2
1=2
e-n basis:
Type: natural power
Order: 8
e-n cutoff:
Type: alt polynomial
TERM 3:
Rank:
2
1
Rules:
n3=n4
n3=n5
n3=n6
n3=n7
n3=n8
n1=n2
1-n3=2-n3
1-n1=2-n1
1-1=2-2
e-e basis:
Type: natural power
Order: 4
e-n basis:
Type: natural power
Order: 4
e-n cutoff:
Type: alt polynomial
Title: ''
``````
It seems to me that the e-e-n JASTROW term for the light atoms gives very poor results, but is it worth to apply it if the molecule consists only of light atoms like B and H.
Which set of atoms can be excluded from e-e-n term optimization?

Any suggestions.

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Pablo_Lopez_Rios
Posts: 52
Joined: Thu Jan 30, 2014 1:25 am

### Re: Diborane Jastrow optimization

How many configurations are you using for the optimization? Have you tried fixing the Jastrow cut-off values (I would expect L=3-5 a.u. to be OK values for isotropic terms in molecules)?

Also, you are treating all six hydrogens as equivalent, but to me it looks like n3=n4 and n5=n6=n7=n8 would better describe the symmetry of the molecule.

The statistical efficiency of DMC depends on the quality of the trial wave function, so it's probably a good idea to make sure you have a good Jastrow factor before attempting to converge your DMC results.

Best,
Pablo
Hey there! I am using CASINO.
Posts: 138
Joined: Wed Apr 15, 2015 3:14 pm

### Re: Diborane Jastrow optimization

Perhaps I understood why this is so.

Caperley proved in https://link.springer.com/article/10.1007/BF02628307 that VAR_DMC ~ 2 (E_VMC - E_DMC)/dtdmc, keep in a mind that VAR_DMC = N_corr * VAR_VMC.
where N_corr - DMC N_corr
One can rewrite equation as:

N_corr * dtdmc = 2 (E_VMC - E_DMC)/VAR_VMC

If we assume that DMC and VMC are size consistent methods (why not?) then for the system of N equivalent atoms numerator and denominator should increase proportionately and N_corr * dtdmc remains the same. if I neglect the presence of B atoms, then N_corr * dtdmc for H2 and B2H6 shoul be the same (look at graph).

But existence of B atoms requests mush smaller dtdmc (25 times smaller than for H atom), so I've got very large N_corr.

Thus transition metal hydrides like https://en.wikipedia.org/wiki/Potassium ... idorhenate are very bad case for QMC.

PS. sup and sub BBCode tags should be very usefull in this forum.
Attachments
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Pablo_Lopez_Rios
Posts: 52
Joined: Thu Jan 30, 2014 1:25 am

### Re: Diborane Jastrow optimization

Yes, you quote is a well-known result, which I was in fact making use of in my earlier reply -- E_DMC itself is independent of the Jastrow factor (it does not change the nodes of the wave function), but the better the Jastrow factor, the smaller the difference E_VMC - E_DMC, the smaller the variance of the DMC sample of local energies, and the more efficient your DMC calculation is.

The 1/dtdmc factor is clearly problematic for transition metals, as you say, and for this reason these are usually treated using pseudopotentials. But at Z=5 I don't see that Boron could really be considered a difficult case for all-electron DMC.

Going back to your optimization runs, I'd be interested in knowing what specific trouble you are having. Have you tried the "Rules" I suggested? How many configurations are there in your optimization sample?

Best,
Pablo
Hey there! I am using CASINO.
Posts: 138
Joined: Wed Apr 15, 2015 3:14 pm

### Re: Diborane Jastrow optimization

Yes, you quote is a well-known result, which I was in fact making use of in my earlier reply -- E_DMC itself is independent of the Jastrow factor (it does not change the nodes of the wave function), but the better the Jastrow factor, the smaller the difference E_VMC - E_DMC, the smaller the variance of the DMC sample of local energies, and the more efficient your DMC calculation is.

The 1/dtdmc factor is clearly problematic for transition metals, as you say, and for this reason these are usually treated using pseudopotentials. But at Z=5 I don't see that Boron could really be considered a difficult case for all-electron DMC.

Going back to your optimization runs, I'd be interested in knowing what specific trouble you are having. Have you tried the "Rules" I suggested? How many configurations are there in your optimization sample?

Best,
Pablo
Yes, Pablo. I've tried a different types of JASTROW optimizations and yours and r/(r^b+a) power for e-e term as well. This is the best result that can be obtained. No way to improve it.
This molecule has too little correlation energy.
What is the correlation length for the exact JASTROW? The more precise JASTROW the bigger correlation length.

In Soviet Russia Casino plays you.
Pablo_Lopez_Rios
Posts: 52
Joined: Thu Jan 30, 2014 1:25 am

### Re: Diborane Jastrow optimization

After a quick go at this molecule I get:

Code: Select all

``````VMC #1: E     = -52.828(4) ; var  = 11.0(2) (parameters.0.casl)
VMC #2: E     = -53.1826(7) ; var  = 0.672(8) (parameters.1.casl)
VMC #3: E     = -53.1823(7) ; var  = 0.68(1) (parameters.2.casl)
VMC #4: E     = -53.2012(7) ; var  = 0.801(8) (parameters.3.casl)
VMC #5: E     = -53.2027(7) ; var  = 0.81(2) (parameters.4.casl)
``````
which looks pretty reasonable to me. What do you get?

Pablo
Hey there! I am using CASINO.
Posts: 138
Joined: Wed Apr 15, 2015 3:14 pm

### Re: Diborane Jastrow optimization

Accidentally in my molecular database B2H6 geometry was in Bohr, but other 140 molecules geometry in Angstrom.
Automated script doesn't took it into account. That's an epic fail. I'am sorry.

For the right geometry I've got:

Code: Select all

``````VMC #1: E     = -52.78(3) ; var  = 4.1(1) (parameters.0.casl)
VMC #2: E     = -53.14(1) ; var  = 0.98(2) (parameters.1.casl)
VMC #3: E     = -53.218(9) ; var  = 0.59(2) (parameters.2.casl)
VMC #4: E     = -53.199(9) ; var  = 0.56(2) (parameters.3.casl)
VMC #5: E     = -53.220(8) ; var  = 0.52(1) (parameters.4.casl)
VMC #6: E     = -53.221(9) ; var  = 0.51(1) (parameters.5.casl)
VMC #7: E     = -53.221(8) ; var  = 0.54(3) (parameters.6.casl)
VMC #8: E     = -53.207(8) ; var  = 0.53(1) (parameters.7.casl)
VMC #9: E     = -53.226(9) ; var  = 0.53(2) (parameters.8.casl)
VMC #10: E     = -53.22(1) ; var  = 0.48(2) (parameters.9.casl)
``````
and reasonable DMC energy, N_corr, etc...

Thank you, Pablo for the productive discussion.