PCh10 15 lec 2 - Revision history

Bes: /* Comparison of theoretical Models and Chosen Basis Sets (Sec 15.8) */

2020-05-04T15:22:57Z

Comparison of theoretical Models and Chosen Basis Sets (Sec 15.8)

Bes: /* Continuing with Chapter 10/15...more about wavefunctions */

2020-05-04T15:19:41Z

Continuing with Chapter 10/15...more about wavefunctions

Bes: /* WebMO Wavefunctions */

2020-05-04T15:18:06Z

WebMO Wavefunctions

Bes: /* WebMO Wavefunctions */

2020-05-04T15:09:28Z

WebMO Wavefunctions

Bes: /* WebMO Wavefunctions */

2020-05-04T14:58:08Z

WebMO Wavefunctions

Bes: /* Continuing with Chapter 10/15...more about wavefunctions */

2020-05-04T14:53:30Z

Continuing with Chapter 10/15...more about wavefunctions

Bes: /* Continuing with Chapter 10/15...more about wavefunctions */

2020-05-04T14:42:23Z

Continuing with Chapter 10/15...more about wavefunctions

Bes: /* Continuing with Chapter 10/15...more about wavefunctions */

2020-05-04T14:42:03Z

Continuing with Chapter 10/15...more about wavefunctions

Bes: /* Continuing with Chapter 10/15...more about wavefunction */

2020-05-04T14:40:55Z

Continuing with Chapter 10/15...more about wavefunction

Bes: /* Continuing with Chapter 10/15...more about wavefunction */

2020-05-04T14:16:54Z

Continuing with Chapter 10/15...more about wavefunction

@@ Line 44: / Line 44: @@
 :- '''Accurate: 6-311G+(2d,p)''': this is an even more involved "split-valence" basis set that now includes polarizing functions as well as other "diffuse" functions. In a 6-311G+(2d, p), the core electron wavefunctions are estimated using 6 Gaussians, the "first inner core" valence electron wavefunctions are estimated using 3 Gaussians, the "second inner core" valence electron wavefunctions are estimated using 1 Gaussian, and the "outer" valence electron wavefunctions are estimated using 1. The details of the polarizing and diffuse functions is beyond our conversation at this point.
-==Comparison of theoretical Models and Chosen Basis Sets (Sec 15.8)==
+==Review Figures...==
-This section has a collection of tables comparing different level sof theory and basis sets. Please skim these...more later.
+Please read the figure caption of the following figures to see how Gaussian Functions are being used to estimate the atomic wavefunctions:
 End of lecture.

@@ Line 27: / Line 27: @@
 [[File:Screen Shot 2020-05-04 at 9.38.00 AM.png|200px]]
 :- where:
-:::''φ<sub>j</sub> (r)'' is the estimated wavefunction (the solution)
+:::''φ<sub>j</sub> (r)'' is the estimated wavefunction (the solution),
-:::''f<sub>i</sub> (r)'' is the Gaussian function
+:::''f<sub>i</sub> (r)'' is the Gaussian function containing the ''ζ'' term,
-:::''c<sub>i</sub>'' is the weighting factor
+:::''c<sub>i</sub>'' is the weighting factor.
 ===WebMO Wavefunctions===

← Older revision		Revision as of 15:18, 4 May 2020
Line 41:		Line 41:

	''Note: if you are conducting a calculation for an atom like CH<sub>4</sub>, then at minimum you need a 1s-orbitals to describe the H-atoms, and 1s-orbital, 2s-orbital and 2p-orbitals to describe the C-atom. If the wavefunction only uses estimations for the 1s, 2s, 2 p orbitals we would refer to this as the "minimum" number of orbitals that could be used in this calculation...anything less would not accomodate all of the electrons. The "STO-3G and 3-21G/X-YZG are minimum basis sets." If great flexibility in your calculation is required, then even for something like CH<sub>4</sub>, we include Gaussian functions to estimate the d-orbitals. The addition of d-orbitals in the calculation allows for some asymmetry in the electron density.''		''Note: if you are conducting a calculation for an atom like CH<sub>4</sub>, then at minimum you need a 1s-orbitals to describe the H-atoms, and 1s-orbital, 2s-orbital and 2p-orbitals to describe the C-atom. If the wavefunction only uses estimations for the 1s, 2s, 2 p orbitals we would refer to this as the "minimum" number of orbitals that could be used in this calculation...anything less would not accomodate all of the electrons. The "STO-3G and 3-21G/X-YZG are minimum basis sets." If great flexibility in your calculation is required, then even for something like CH<sub>4</sub>, we include Gaussian functions to estimate the d-orbitals. The addition of d-orbitals in the calculation allows for some asymmetry in the electron density.''
		+
		+	:- '''Accurate: 6-311G+(2d,p)''': this is an even more involved "split-valence" basis set that now includes polarizing functions as well as other "diffuse" functions. In a 6-311G+(2d, p), the core electron wavefunctions are estimated using 6 Gaussians, the "first inner core" valence electron wavefunctions are estimated using 3 Gaussians, the "second inner core" valence electron wavefunctions are estimated using 1 Gaussian, and the "outer" valence electron wavefunctions are estimated using 1. The details of the polarizing and diffuse functions is beyond our conversation at this point.
		+
		+	==Comparison of theoretical Models and Chosen Basis Sets (Sec 15.8)==
		+	This section has a collection of tables comparing different level sof theory and basis sets. Please skim these...more later.
		+
		+	End of lecture.

@@ Line 37: / Line 37: @@
 You have been using WebMO for quite some time and now i can explain to you the names of the "Basis Sets" (sec 15.7)
 :- '''Minimum: STO-3G''': the "3G" means that all electron wavefunctions are estimated using 3-Gaussian functions. The STO (Slater-type orbitals) makes historical reference to  a more complicated function (eq. 15.53) that has now been replaced with these Gaussians. Yes, there are STO-1G or STO-4G, or even STO-5G basic sets where the STO function is estimated with 1, 4, or 5 Gaussians; these are all not so great...there are better ways to do this...
-:- '''Basic: 3-21'': this is a "split-valence" basis set, where the valence electrons (inner and outer) and core electrons are treated differently. in a 3-21, the core electron wavefunctions are estimated using 3 Gaussians, the "inner core" valence electron wavefunctions are estimated using 2 Gaussians, and the "outer" valence electron wavefunctions are estimated using only 1 Gaussian function.
+:- '''Basic: 3-21G''': this is a "split-valence" basis set, where the valence electrons (inner and outer) and core electrons are treated differently. in a 3-21, the core electron wavefunctions are estimated using 3 Gaussians, the "inner core" valence electron wavefunctions are estimated using 2 Gaussians, and the "outer" valence electron wavefunctions are estimated using only 1 Gaussian function.

@@ Line 36: / Line 36: @@
 You have been using WebMO for quite some time and now i can explain to you the names of the "Basis Sets" (sec 15.7)
-:- Minimum Basis Set: STO-3G: the "3G" means that the wavefunctions are estimated using 3-Gaussian functions. The STO (Slater-type orbitals) makes historical reference to  a more complicated function (eq. 15.53) that has now been replaced with these Gaussians. Yes, there are STO-1G or STO-4G, or even STO-5G basic sets where the STO function is estimated with 1, 4, or 5 Gaussians; these are all not so great...there are better ways to do this...
+:- '''Minimum: STO-3G''': the "3G" means that all electron wavefunctions are estimated using 3-Gaussian functions. The STO (Slater-type orbitals) makes historical reference to  a more complicated function (eq. 15.53) that has now been replaced with these Gaussians. Yes, there are STO-1G or STO-4G, or even STO-5G basic sets where the STO function is estimated with 1, 4, or 5 Gaussians; these are all not so great...there are better ways to do this...
-:-
+:- '''Basic: 3-21'': this is a "split-valence" basis set, where the valence electrons (inner and outer) and core electrons are treated differently. in a 3-21, the core electron wavefunctions are estimated using 3 Gaussians, the "inner core" valence electron wavefunctions are estimated using 2 Gaussians, and the "outer" valence electron wavefunctions are estimated using only 1 Gaussian function.

← Older revision		Revision as of 14:53, 4 May 2020
Line 30:		Line 30:
	:::''f<sub>i</sub> (r)'' is the Gaussian function		:::''f<sub>i</sub> (r)'' is the Gaussian function
	:::''c<sub>i</sub>'' is the weighting factor		:::''c<sub>i</sub>'' is the weighting factor
		+
		+	===WebMO Wavefunctions===
		+	[[File:Screen Shot 2020-04-16 at 7.51.30 AM.png\|300px]]
		+
		+
		+	You have been using WebMO for quite some time and now i can explain to you the names of the "Basis Sets" (sec 15.7)
		+	:- Minimum Basis Set: STO-3G: the "3G" means that the wavefunctions are estimated using 3-Gaussian functions. The STO (Slater-type orbitals) makes historical reference to a more complicated function (eq. 15.53) that has now been replaced with these Gaussians. Yes, there are STO-1G or STO-4G, or even STO-5G basic sets where the STO function is estimated with 1, 4, or 5 Gaussians; these are all not so great...there are better ways to do this...
		+	:-

@@ Line 25: / Line 25: @@
 First, these Exp(-r<sup>2</sup>) functions are Gaussian functions. If we use only one Gaussian function to replace the Exp(-r) function, then we get a really bad answer. So what we do is use more than one Gaussian function...or we use a '''''linear combination of Gaussian functions''''' to estimate the Exp(-r) function.
-[[File:Screen Shot 2020-05-04 at 9.38.00 AM.png|400px]]
+[[File:Screen Shot 2020-05-04 at 9.38.00 AM.png|300px]]
 :- where:
-:::''φ<sub>j</sub>(r)'' is the estimated wavefunction
+:::''φ<sub>j</sub> (r)'' is the estimated wavefunction (the solution)
-:::''f<sub>i</sub>(r)'' is the Gaussian function
+:::''f<sub>i</sub> (r)'' is the Gaussian function
-:::c<sub>i</sub> is the weighting factor
+:::''c<sub>i</sub>'' is the weighting factor

@@ Line 17: / Line 17: @@
 We are scheduled to have the final exam on Sat, May 9th. I have not yet worked on this, but i hope to have it "ready" by Sat am and then collect it by Weds, May 13th at 5pm.
-==Continuing with Chapter 10/15...more about wavefunction==
+==Continuing with Chapter 10/15...more about wavefunctions==
 So, recall that we are working under the conditions of the "orbital approximation" (Sec 10.1), ie, the hydrogen atom wavefunctions are not a bad place to start to figure out numerically what the multi-electron wavefunctions should look like. We have made our first adjustment to these H-atom wavefunctions by replacing the nuclear charge (''Z'') with (''ζ'')...
 [[File:Screen Shot 2020-04-27 at 9.48.37 AM.png|400 px]]