CamCASP/Programming/7 - Revision history

import>Am592: /* Numerical Integrals */

2013-10-23T17:37:49Z

Numerical Integrals

@@ Line 103: / Line 103: @@
 </pre>
 The reference values use very large grids and result in dipole-dipole polarizabiliites that are fairly insensitive to the Becke parameter. There is a larger variation for the smaller grid, with the agreement getting rather good for smaller values. --[[User:am592|alston]] 18:55, 3 May 2010 (BST)
 =Kernel Notation=

import>Am592: /* To Do & Thoughts */

2010-05-17T13:29:49Z

To Do & Thoughts

← Older revision		Revision as of 13:29, 17 May 2010
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	A_{k,k'} = -4 \sum_{ar} D_{ar,k} D_{ar,k'} \frac{(e_r - e_a)}{(e_r-e_a)^2 - w^2}		A_{k,k'} = -4 \sum_{ar} D_{ar,k} D_{ar,k'} \frac{(e_r - e_a)}{(e_r-e_a)^2 - w^2}
	</math>		</math>
	This is a rather simple term ~~to evaluate~~, but it takes a while to evaluate becuase it must be done for every pair of auxiliry basis function. I had naively assumed that some sort of pre-screening might work for this; something along the lines described above. Yes, there is no reason to assume this as there is no underlying integral to screen. But if we assume that for basis functions ''far away'' (in the overap sense) <math>A_{k,k}=0</math> we get garbage. The elements of <math>A</math> don't seem to have any correlation with the overlap of basis functions <math>\int \chi_k \chi_{k'} dr</math>. Well, I don't know what's to be done about this. It seems to me that the solution may be to first make the DF linear-scaling (using local auxiliary basis sets), though I can't say how this would help here...		This is a rather simple term, but it takes a while to evaluate becuase it must be done for every pair of auxiliry basis function. I had naively assumed that some sort of pre-screening might work for this; something along the lines described above. Yes, there is no reason to assume this as there is no underlying integral to screen. But if we assume that for basis functions ''far away'' (in the overap sense) <math>A_{k,k}=0</math> we get garbage. The elements of <math>A</math> don't seem to have any correlation with the overlap of basis functions <math>\int \chi_k \chi_{k'} dr</math>. Well, I don't know what's to be done about this. It seems to me that the solution may be to first make the DF linear-scaling (using local auxiliary basis sets), though I can't say how this would help here...
	* Hybrid functionals in new propagator module.		* Hybrid functionals in new propagator module.

import>Am592: /* To Do */

2010-05-17T13:27:04Z

To Do

@@ Line 30: / Line 30: @@
 --[[User:am592|alston]] 19:15, 27 April 2010 (BST)
-=To Do=
+=To Do & Thoughts=
 * Use screening when calculating kernel integrals. Probably use the overlap matrix as a screen.
 =Concerns=

import>Am592: /* Status */

2010-05-10T16:26:06Z

Status

← Older revision		Revision as of 16:26, 10 May 2010
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	* Coded for closed-shell systems.		* Coded for closed-shell systems.
	--[[User:am592\|alston]] 19:15, 27 April 2010 (BST)		--[[User:am592\|alston]] 19:15, 27 April 2010 (BST)

			=To Do=
			* Use screening when calculating kernel integrals. Probably use the overlap matrix as a screen.
			* Hybrid Hessians in new propagator module.

	=Concerns=		=Concerns=

import>Am592: /* XVI dimer */

2010-05-05T13:33:27Z

XVI dimer

← Older revision		Revision as of 13:33, 5 May 2010
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	PBE AC ALDAX -6.093 -10.207 -25.394 18.867 8.332 1.940 -12.554 4.5% 12h 11h45m (Dalton no direct, conv 10-6)		PBE AC ALDAX -6.093 -10.207 -25.394 18.867 8.332 1.940 -12.554 4.5% 12h 11h45m (Dalton no direct, conv 10-6)
	</pre>		</pre>
	~~There~~ is only a 0.5 kJ/mol difference in the dispersion energy. Most of the error arises from the electrostatic, induction and exchange energies - all, I'm sure, because of the lack of the asymptotic correction. There is a substantial decrease in the time taken per job when the ALDAX kernel is used. The lack of AC also contributes. DALTON takes a total of 18h to calculate the Kernel integrals. CamCASP takes 3h46m. This is the biggest time reduction.		With PBE/noAC-ALDAX there is only a 0.5 kJ/mol difference in the dispersion energy. Most of the error arises from the electrostatic, induction and exchange energies - all, I'm sure, because of the lack of the asymptotic correction. There is a substantial decrease in the time taken per job when the ALDAX kernel is used. The lack of AC also contributes. DALTON takes a total of 18h to calculate the Kernel integrals. CamCASP takes 3h46m. This is the biggest time reduction.
			PBE/AC-ALDAX is probably the way to go. The large errors in the exchange energies that we see with PBE/noAC are largely corrected with the AC. The error in the interaction energy is now under 5%. This is acceptable. Also, without the .DIRECT option, DALTON seems quite fast and is able to implement the AC in almost the same time.
	* Geometry 2:		* Geometry 2:
	<pre>		<pre>

import>Am592: /* XVI dimer */

2010-05-05T12:07:51Z

XVI dimer

← Older revision		Revision as of 12:07, 5 May 2010
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	<pre>		<pre>
	elst ind2C disp2C exch exind2C exdisp2C Total Diff Timings (DAL,CamCASP)		elst ind2C disp2C exch exind2C exdisp2C Total Diff Timings (DAL,CamCASP)
	PBE0 AC ALDA+CHF -6.114 -10.220 -25.462 18.197 8.448 2.002 -13.149 36h 11h20m		PBE0 AC ALDA+CHF -6.114 -10.220 -25.462 18.197 8.448 2.002 -13.149 36h 11h20m (Dalton direct, conv 10-7)
	PBE noAC ALDAX -6.563 -11.424 -25.981 20.223 9.529 2.092 -12.125 7.8% 11h45m 12h56m		PBE noAC ALDAX -6.563 -11.424 -25.981 20.223 9.529 2.092 -12.125 7.8% 11h45m 12h56m (Dalton direct, conv 10-7)
	PBE AC ALDAX -6.093 -10.207 -25.394 18.867 8.332 1.940 -12.554 4.5% 12h 11h45m (Dalton no direct, conv 10-6)		PBE AC ALDAX -6.093 -10.207 -25.394 18.867 8.332 1.940 -12.554 4.5% 12h 11h45m (Dalton no direct, conv 10-6)
	</pre>		</pre>
	There is only a 0.5 kJ/mol difference in the dispersion energy. Most of the error arises from the electrostatic, induction and exchange energies - all, I'm sure, because of the lack of the asymptotic correction. There is a substantial decrease in the time taken per job when the ALDAX kernel is used. The lack of AC also contributes. DALTON takes a total of 18h to calculate the Kernel integrals. CamCASP takes 3h46m. This is the biggest time reduction.		There is only a 0.5 kJ/mol difference in the dispersion energy. Most of the error arises from the electrostatic, induction and exchange energies - all, I'm sure, because of the lack of the asymptotic correction. There is a substantial decrease in the time taken per job when the ALDAX kernel is used. The lack of AC also contributes. DALTON takes a total of 18h to calculate the Kernel integrals. CamCASP takes 3h46m. This is the biggest time reduction.

import>Am592: /* XVI dimer */

2010-05-05T12:04:45Z

XVI dimer

← Older revision		Revision as of 12:04, 5 May 2010
Line 242:		Line 242:
	PBE0 AC ALDA+CHF -6.114 -10.220 -25.462 18.197 8.448 2.002 -13.149 36h 11h20m		PBE0 AC ALDA+CHF -6.114 -10.220 -25.462 18.197 8.448 2.002 -13.149 36h 11h20m
	PBE noAC ALDAX -6.563 -11.424 -25.981 20.223 9.529 2.092 -12.125 7.8% 11h45m 12h56m		PBE noAC ALDAX -6.563 -11.424 -25.981 20.223 9.529 2.092 -12.125 7.8% 11h45m 12h56m
			PBE AC ALDAX -6.093 -10.207 -25.394 18.867 8.332 1.940 -12.554 4.5% 12h 11h45m (Dalton no direct, conv 10-6)
	</pre>		</pre>
	There is only a 0.5 kJ/mol difference in the dispersion energy. Most of the error arises from the electrostatic, induction and exchange energies - all, I'm sure, because of the lack of the asymptotic correction. There is a substantial decrease in the time taken per job when the ALDAX kernel is used. The lack of AC also contributes. DALTON takes a total of 18h to calculate the Kernel integrals. CamCASP takes 3h46m. This is the biggest time reduction.		There is only a 0.5 kJ/mol difference in the dispersion energy. Most of the error arises from the electrostatic, induction and exchange energies - all, I'm sure, because of the lack of the asymptotic correction. There is a substantial decrease in the time taken per job when the ALDAX kernel is used. The lack of AC also contributes. DALTON takes a total of 18h to calculate the Kernel integrals. CamCASP takes 3h46m. This is the biggest time reduction.

import>Am592: /* Numerical Integrals */

2010-05-03T18:16:44Z

Numerical Integrals

← Older revision		Revision as of 18:16, 3 May 2010
Line 47:		Line 47:
	* EFFICIENCY: The grid consists of atomic grids. Connected atoms share points. So the grid contains several instances of points. This is very wasteful. There must be some way of reducing the atom grids into one molecular grid. I must look into it.		* EFFICIENCY: The grid consists of atomic grids. Connected atoms share points. So the grid contains several instances of points. This is very wasteful. There must be some way of reducing the atom grids into one molecular grid. I must look into it.
	* ACCURACY: We can achieve 4 decimal numerical accuracy for the dipole polarizability of water if we use very large grids (400 radial, 600 angular). For such grids, the Becke smoothing parameter doesn't change results (I used parameter values of 2, 4 and 10). But even with this large grids, the quadrupole polarizabilities differ in the second or third place as the smoothing parameter is varied.		* ACCURACY: We can achieve 4 decimal numerical accuracy for the dipole polarizability of water if we use very large grids (400 radial, 600 angular). For such grids, the Becke smoothing parameter doesn't change results (I used parameter values of 2, 4 and 10). But even with this large grids, the quadrupole polarizabilities differ in the second or third place as the smoothing parameter is varied.
	* APPROXIMATIONS: Using extremely large grids is not practical. So we must compromise. For a given choice of KernelEps and grid size (60 radial and 100 angular) what Becke smoothing parameter is appropriate? Based on the dipole-dipole polarizabilities of water, it seems like a value around 4 is appropriate. This is the default. Larger values (~10) cause significant change to the polarizability anisotropy. Smaller values (~2) seem to result in slightly larger errors in the quadrupole polarizabilities, but these are not quite significant enough. So, I'd say a value of 2 to 4 should be OK.		* APPROXIMATIONS: Using extremely large grids is not practical. So we must compromise. For a given choice of KernelEps and grid size (60 radial and 100 angular) what Becke smoothing parameter is appropriate? Based on the dipole-dipole polarizabilities of water, it seems like a value around 4 is appropriate. This is the default. Larger values (~10) cause significant change to the polarizability anisotropy. Smaller values (~2) seem to result in slightly larger errors in the quadrupole polarizabilities, but these are not quite significant enough. So, I'd say a value of 2 to 4 should be OK. The default value is 3.
	<pre>		<pre>
	Water aTZ/aTZ PBE0/AC ALDAX		Water aTZ/aTZ PBE0/AC ALDAX

import>Am592: /* Numerical Integrals */

2010-05-03T17:55:45Z

Numerical Integrals

← Older revision		Revision as of 17:55, 3 May 2010
Line 65:		Line 65:
	--------------------------------------------------		--------------------------------------------------
	</pre>		</pre>
	The reference values use very large grids and result in dipole-dipole polarizabiliites that are fairly insensitive to the Becke parameter. There is a larger variation for the smaller grid, with the agreement getting rather good for smaller values.		The reference values use very large grids and result in dipole-dipole polarizabiliites that are fairly insensitive to the Becke parameter. There is a larger variation for the smaller grid, with the agreement getting rather good for smaller values. --[[User:am592\|alston]] 18:55, 3 May 2010 (BST)

	=Kernel Notation=		=Kernel Notation=

import>Am592: /* Numerical Integrals */

2010-05-03T17:55:20Z

Numerical Integrals

← Older revision		Revision as of 17:55, 3 May 2010
Line 49:		Line 49:
	* APPROXIMATIONS: Using extremely large grids is not practical. So we must compromise. For a given choice of KernelEps and grid size (60 radial and 100 angular) what Becke smoothing parameter is appropriate? Based on the dipole-dipole polarizabilities of water, it seems like a value around 4 is appropriate. This is the default. Larger values (~10) cause significant change to the polarizability anisotropy. Smaller values (~2) seem to result in slightly larger errors in the quadrupole polarizabilities, but these are not quite significant enough. So, I'd say a value of 2 to 4 should be OK.		* APPROXIMATIONS: Using extremely large grids is not practical. So we must compromise. For a given choice of KernelEps and grid size (60 radial and 100 angular) what Becke smoothing parameter is appropriate? Based on the dipole-dipole polarizabilities of water, it seems like a value around 4 is appropriate. This is the default. Larger values (~10) cause significant change to the polarizability anisotropy. Smaller values (~2) seem to result in slightly larger errors in the quadrupole polarizabilities, but these are not quite significant enough. So, I'd say a value of 2 to 4 should be OK.
	<pre>		<pre>
	Water aTZ/aTZ PBE0/AC		Water aTZ/aTZ PBE0/AC ALDAX
	Radial Angular Becke KernelEps alpha anisotropy		Radial Angular Becke KernelEps alpha anisotropy
	==================================================		==================================================
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	200 400 10 1.0e-8 8.2392 1.0238		200 400 10 1.0e-8 8.2392 1.0238
	200 400 2 1.0e-8 8.2391 1.0239		200 400 2 1.0e-8 8.2391 1.0239
	--------------------------------------------------		--------------------------------------------------
			60 100 10 1.0e-8 8.2409 1.0178

			60 100 4 1.0e-8 8.2387 1.0235
			60 100 2 1.0e-8 8.2386 1.0237
			--------------------------------------------------
	</pre>		</pre>
			The reference values use very large grids and result in dipole-dipole polarizabiliites that are fairly insensitive to the Becke parameter. There is a larger variation for the smaller grid, with the agreement getting rather good for smaller values.

	=Kernel Notation=		=Kernel Notation=