CamCASP/Programming/1 - Revision history

import>Am592: /* GAMESS(US) */

2011-12-08T16:40:15Z

GAMESS(US)

← Older revision		Revision as of 16:40, 8 December 2011
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	I'm not sure what Cartesian GTOs GAMESS(US) uses, but they must be similar to those we get from GAMINT as this integral module is a modified version of GAMESS(US). The order is certainly the same as that used by GAMINT, but the normalization could be different.		I'm not sure what Cartesian GTOs GAMESS(US) uses, but they must be similar to those we get from GAMINT as this integral module is a modified version of GAMESS(US). The order is certainly the same as that used by GAMINT, but the normalization could be different.

	GAMESS(US) uses Spherical GTOs in a slightly different way from other codes. The MO coefficients of its spherical GTOs are not supplied as standing in front of the components of the spherical GTOs, but rather they stand in front of the Cartesian components. To make this concrete, rather than supply 5 sets of 5 MO coefficients for a spherical d-function (each set of 5 would correspond to an MO), GAMESS(US) will supply 5 sets of '''6''' coefficients. Each of these 6 would stand in front of Cartesian GTOs. This is OK, but the normalization of these Cartesian GTOs is rather awkward. I have worked out the transformation matrices from these Cartesian GTOs to an equivalent spherical set. I won't put any details here as I still don't understand exactly what's going on. See details in the Interfaces section.		GAMESS(US) uses Spherical GTOs in a slightly different way from other codes. The MO coefficients of its spherical GTOs are not supplied as standing in front of the components of the spherical GTOs, but rather they stand in front of the Cartesian components. To make this concrete, rather than supply 5 sets of 5 MO coefficients for a spherical d-function (each set of 5 would correspond to an MO), GAMESS(US) will supply 5 sets of '''6''' coefficients. Each of these 6 would stand in front of Cartesian GTOs. This is OK, but the normalization of these Cartesian GTOs is rather awkward. I have worked out the transformation matrices from these Cartesian GTOs to an equivalent spherical set. I won't put any details here as I still don't understand exactly what's going on. See details in the [[ CamCASP/Interfaces \| Interfaces ]] section.

	==NWChem==		==NWChem==

import>Am592: /* DALTON */

2011-12-08T16:38:47Z

DALTON

@@ Line 64: / Line 64: @@
    \times G^D_{ijk}(r,\alpha,A)
 </math>
 ==GAMINT==

import>Am592: /* GAMINT */

2009-05-12T13:43:01Z

GAMINT

← Older revision		Revision as of 13:43, 12 May 2009
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	\times G^G_{ijk}(r,\alpha,A)		\times G^G_{ijk}(r,\alpha,A)
	</math>		</math>

			This can be achieved using '''norm_contraction_coeffs''' to obtain the first term and '''norm_integral1''' or '''norm_integral2''' for the second term.

	Remember, we haven't talked about the ''order'' of the symmetry components yet. These are different in DALTON and GAMINT. More on this later.		Remember, we haven't talked about the ''order'' of the symmetry components yet. These are different in DALTON and GAMINT. More on this later.

import>Am592: /* GAUSSINT */

2009-05-12T13:35:10Z

GAUSSINT

← Older revision		Revision as of 13:35, 12 May 2009
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	</math>		</math>

	The first term defines the Cartesian to Spherical transformation matrices (we haven't yet discussed the order) '''BUT''' these are different from those used to go from GAMINT to DALTON: There is no factor of <math>1/\sqrt{(2l-1)!!}</math> present here. So the transformation matrices defined in '''module basis_trans_mats''' are not correct as they include this factor. ~~To avoid this sort of complication, we use '''function norm_gaussint''' (in integrals.F90) to include the following normalization to integrals calculated with GAUSSINT:~~		The first term defines the Cartesian to Spherical transformation matrices (we haven't yet discussed the order) '''BUT''' these are different from those used to go from GAMINT to DALTON: There is no factor of <math>1/\sqrt{(2l-1)!!}</math> present here. So the transformation matrices defined in '''module basis_trans_mats''' are not correct as they include this factor.

			To avoid this sort of complication, we use '''function norm_gaussint''' (in integrals.F90) to include the following normalization to integrals calculated with GAUSSINT:
	* Spherical GTOs: <math>\sqrt{(2l-1)!!}</math>		* Spherical GTOs: <math>\sqrt{(2l-1)!!}</math>
	* Cartesian GTOs: <math>\frac{(2l-1)!!}{(2j-1)!!(2j-1)!!(2k-1)!!}</math>		* Cartesian GTOs: <math>\sqrt{\frac{(2l-1)!!}{(2j-1)!!(2j-1)!!(2k-1)!!}}</math>

			For spherical GTOs, this means that the Cartesian to Spherical transformation matrices with the factor
⚫	The ~~last~~ term is included in the contraction coefficients by subroutine '''norm_contraction_coeffs''' which is in '''module gamint_frontend'''.
			<math>1/\sqrt{(2l-1)!!}</math> can be used as our new transformation to spherical GTOs is

			<math>
	And to transform the Cartesian GTOs into the form used by DALTON we need to use the transformation
			G_{lm}(r,\alpha,A) = \sum_{ijk} \frac{C_{lm;ijk}}{\sqrt{(2l-1)!!}}
			\times \left( \frac{2\alpha}{\pi}\right)^{3/4}
			\sqrt{
			\frac{(4\alpha)^l}{(2l-1)!!}
			}
			\times \sqrt{(2l-1)!!}
			\times G^{\rm GAU}_{ijk}(r,\alpha,A)
			</math>

		⚫	So, the first term is the standard spherical to Cartesian transformation matrix. The second term is included in the contraction coefficients by subroutine '''norm_contraction_coeffs''' which is in '''module gamint_frontend'''. And the last term is included using '''function norm_gaussint'''.

			For Cartesian GTOs, the normalization included using '''function norm_gaussint''' results in GTOs of the form:

	<math>		<math>
	~~G^D_~~{ijk}(r,\alpha,A) = \left( \frac{2\alpha}{\pi}\right)^{3/4}		G_{ijk}(r,\alpha,A) = \left( \frac{2\alpha}{\pi}\right)^{3/4}
	\sqrt{		\sqrt{
	\frac{(4\alpha)^l}{(2l-1)!!}		\frac{(4\alpha)^l}{(2l-1)!!}
	}		}
	\times \sqrt{(2l-1)!!}		\times \sqrt{\frac{(2l-1)!!}{(2j-1)!!(2j-1)!!(2k-1)!!}}
	\times G^{\rm GAU}_{ijk}(r,\alpha,A)		\times G^{\rm GAU}_{ijk}(r,\alpha,A)
	</math>		</math>

			These are fully normalized Cartesian GTOs and are therefore in the correct form for internal use (see below).
	Remember, we haven't talked about the ''order'' of the symmetry components yet. In general, these will be different in DALTON and GAUSSINT. More on this later.

			----

			'''But these are not the correct form for DALTON which uses Cartesian GTOs with a strange normalization. I still have to modify the code to get this correct. However, it is rarely going to be used, so this is not a high priority.'''

			----

	==CamCASP==		==CamCASP==

import>Am592: /* GAUSSINT */

2009-05-12T13:24:23Z

GAUSSINT

← Older revision		Revision as of 13:24, 12 May 2009
Line 124:		Line 124:
	</math>		</math>

	The first term defines the Cartesian to Spherical transformation matrices (we haven't yet discussed the order) '''BUT''' these are different from those used to go from GAMINT to DALTON: There is no factor of <math>1/\sqrt{(2l-1)!!}</math> present here. So the transformation matrices defined in '''module basis_trans_mats''' are not correct as they include this factor.		The first term defines the Cartesian to Spherical transformation matrices (we haven't yet discussed the order) '''BUT''' these are different from those used to go from GAMINT to DALTON: There is no factor of <math>1/\sqrt{(2l-1)!!}</math> present here. So the transformation matrices defined in '''module basis_trans_mats''' are not correct as they include this factor. To avoid this sort of complication, we use '''function norm_gaussint''' (in integrals.F90) to include the following normalization to integrals calculated with GAUSSINT:
			* Spherical GTOs: <math>\sqrt{(2l-1)!!}</math>
			* Cartesian GTOs: <math>\frac{(2l-1)!!}{(2j-1)!!(2j-1)!!(2k-1)!!}</math>

	The last term is included in the contraction coefficients by subroutine '''norm_contraction_coeffs''' which is in '''module gamint_frontend'''.		The last term is included in the contraction coefficients by subroutine '''norm_contraction_coeffs''' which is in '''module gamint_frontend'''.

import>Am592: /* GAUSSINT */

2009-05-12T11:54:53Z

GAUSSINT

← Older revision		Revision as of 11:54, 12 May 2009
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	\frac{(4\alpha)^l}{(2l-1)!!}		\frac{(4\alpha)^l}{(2l-1)!!}
	}		}
	\times \sqrt{(~~2i-1)!!(2j-1)!!(2k~~-1)!!}		\times \sqrt{(2l-1)!!}
	\times G^G_{ijk}(r,\alpha,A)		\times G^{\rm GAU}_{ijk}(r,\alpha,A)
	</math>		</math>

	Remember, we haven't talked about the ''order'' of the symmetry components yet. ~~These~~ ~~are~~ different in DALTON and ~~GAMINT~~. More on this later.		Remember, we haven't talked about the ''order'' of the symmetry components yet. In general, these will be different in DALTON and GAUSSINT. More on this later.

	==CamCASP==		==CamCASP==

import>Am592: /* GAMINT */

2009-05-12T11:48:35Z

GAMINT

← Older revision		Revision as of 11:48, 12 May 2009
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	</math>		</math>

	The first term defines the Cartesian to Spherical transformation matrices (we haven't yet discussed the order). These are defined in '''module basis_trans_mats'''. The second term is needed to remove the extra (double) factorials included by GAMINT. This is taken into account by subroutines '''norm_integral1'''. '''norm_integral2''' and '''calculate_factorial_factors''' all in '''module gamint_frontend'''. And the last term is included in the contraction coefficients by subroutine '''~~norm_denorm_contractions~~''' which is also in '''module gamint_frontend'''.		The first term defines the Cartesian to Spherical transformation matrices (we haven't yet discussed the order). These are defined in '''module basis_trans_mats'''. The second term is needed to remove the extra (double) factorials included by GAMINT. This is taken into account by subroutines '''norm_integral1'''. '''norm_integral2''' and '''calculate_factorial_factors''' all in '''module gamint_frontend'''. And the last term is included in the contraction coefficients by subroutine '''norm_contraction_coeffs''' which is also in '''module gamint_frontend'''.

	And to transform the Cartesian GTOs into the form used by DALTON we need to use the transformation		And to transform the Cartesian GTOs into the form used by DALTON we need to use the transformation
Line 102:		Line 102:

	Remember, we haven't talked about the ''order'' of the symmetry components yet. These are different in DALTON and GAMINT. More on this later.		Remember, we haven't talked about the ''order'' of the symmetry components yet. These are different in DALTON and GAMINT. More on this later.


	==GAUSSINT==		==GAUSSINT==

import>Am592: /* GAUSSINT */

2009-05-12T11:48:14Z

GAUSSINT

@@ Line 105: / Line 105: @@
 ==GAUSSINT==
-This integral code is from the geminal program Robert Bukowski was co-author of. It is slow, but useful as it can calculate a number of integrals. GAUSSINT uses Cartesian GTOs that are completely unnormalized. So all you need to do is include the required normalization factor and you are set. Also, you have to supply the order of the symmetry components to GAUSSINT. More on this later.
+This integral code is from the geminal program Robert Bukowski was co-author of. It is slow, but useful as it can calculate a number of integrals. GAUSSINT uses Cartesian GTOs that are completely unnormalized. But you have to supply the order of the symmetry components to GAUSSINT. More on this later.
 ==CamCASP==

import>Am592: /* Subroutine norm_integrals1 & norm_integrals2 */

2009-04-16T14:20:09Z

Subroutine norm_integrals1 & norm_integrals2

← Older revision		Revision as of 14:20, 16 April 2009
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	</math>		</math>

	=== ~~Subroutine~~ norm_integrals1 & norm_integrals2 ===		=== Subroutines norm_integrals1 & norm_integrals2 ===

	The integrals from GAMINT use Cartesian GTOs with the normalization:		The integrals from GAMINT use Cartesian GTOs with the normalization:

import>Am592: /* Subroutine norm_integrals1 & norm_integrals2 */

2009-04-16T14:19:55Z

Subroutine norm_integrals1 & norm_integrals2

← Older revision		Revision as of 14:19, 16 April 2009
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	The integrals from GAMINT use Cartesian GTOs with the normalization:		The integrals from GAMINT use Cartesian GTOs with the normalization:

			<math>
⚫	!Loop over all cartesian components m in the shell l_m
			G^G_{ijk}(r,\alpha,A) =
⚫	! let powers of x,y,z in this component be i,j,k
			\sqrt{
⚫	! Loop over all cartesian components n in the shell l_n
		⚫	\frac{(2l-1)!!}{(2i-1)!!(2j-1)!!(2k-1)!!}
⚫	! let powers of x,y,z in this component be p,q,r
			}
⚫	! I(m,n) = I(m,n) * sqrt[(2i-1)!!(2j-1)!!(2k-1)!!] *
			x_A^i y_A^j z_A^k e^{-\alpha r_A^2}
	! sqrt[(2p-1)!!(2q-1)!!(2r-1)!!]
			</math>
⚫	! End loop

⚫	!End loop
			These two subroutines remove the factor <math>\sqrt{(2i-1)!!(2j-1)!!(2k-1)!!}</math> from integrals calculated by GAMINT. The algorithm for norm_integrals2 is:
	!

	!The integrals from GAMINT use cartesian gaussians with the normalization:
		⚫	Loop over all cartesian components m in the shell l_m
	! G_ijk =
		⚫	let powers of x,y,z in this component be i,j,k
	! [ (2l-1)!! ]^(1/2)
		⚫	Loop over all cartesian components n in the shell l_n
	! [--------------------------] * x^i y^j z^k exp(-a r^2)
		⚫	let powers of x,y,z in this component be p,q,r
⚫	! [(2i-1)!! (2j-1)!! (2k-1)!!]
		⚫	I(m,n) = I(m,n) * sqrt[(2i-1)!!(2j-1)!!(2k-1)!!] *
	!
	~~!This~~ ~~routine~~ ~~removes~~ ~~the~~ ~~factor~~ [(2i-1)!! (2j-1)!! (2k-1)!!]~~^(-1/2) from~~		sqrt[(2p-1)!!(2q-1)!!(2r-1)!!]
		⚫	End loop
	!these inegrals. The factor [(2l-1)!!]^(1/2) is retained. It can be removed by
		⚫	End loop
	!modifying the contraction coefficients of the basis set using

	!subroutine norm_contraction_coeffs.
			* These routines are needed if spherical GTOs are used as these factors are not present in spherical GTOs.
	!
			* Cartesian GTOs from DALTON: Because DALTON uses Cartesian GTOs without the above factor, integrals from GAMINT must be processed using one of these subroutines to remove this factor '''before''' transforming from the atomic orbital space to the molecular orbital space. See the example in ''subroutine make_T_AO_mono'' in ''module df_Tmat''.