Table 1.P23a shows NPA charges for planar and twisted (C-N rotation) for formamide, 3 -aminoacro

Table 1.P23a shows NPA charges for planar and twisted (C-N...

Key Concepts

Natural Population Analysis (NPA) Charges

NPA charges are a method used in computational chemistry to determine the electron distribution within a molecule by assigning partial charges to atoms. This technique helps in understanding how electrons are delocalized, influencing molecular reactivity, polarity, and intermolecular interactions.

Molecular Conformation (Planar vs. Twisted)

Molecular conformation refers to the spatial arrangement of atoms in a molecule that can change due to rotations around single bonds. The planar versus twisted conformations, especially due to rotations like C-N bond rotation, affect the electronic structure and overall stability, thereby influencing physical and spectroscopic properties.

Chemical Shifts in Nuclear Magnetic Resonance (NMR)

Chemical shifts in NMR, such as those measured for ^17O, are sensitive to the electronic environment surrounding a nucleus, providing insights into molecular structure and dynamics. Variations in chemical shifts help interpret differences in electron density and molecular conformation, aiding in the characterization of molecular species.

Potential Energy Maps and Interaction Potentials

Potential energy maps provide a visual representation of the energy landscape on a molecular surface, showing regions of electron density that can interact with charged particles. These maps are crucial for identifying reactive or binding sites on a molecule and understanding electrostatic interactions between molecules or between a molecule and a probe.

Energy Barriers

Energy barriers represent the energetic differences between various molecular conformations or states, indicating the difficulty of transitioning from one state to another. They are fundamental in understanding reaction kinetics, conformational stability, and the feasibility of electronic reorganization in molecular systems.

Transcript

00:02 Okay, so for this one, you are given the electric field and a cube, and you want to get the flux through the cube.

00:12 I'm just going to reread the question.

00:16 Yes.

00:18 Oh, you want to get the flux of the surface and the net charge for two different electric fields.

00:26 And so the first one, the electric field, is.

00:33 Equal to sorry looking at my notes oh it's three y so in this case it actually depends on space whereas in the previous problem involving this same cube number number six it didn't and so and so now because we don't have a constant field we have to deduce or we can deduce that there might be some charging closed and there might be some non -zero flux.

01:08 So it's 3 .00y in the j -hat direction.

01:14 So i'm going to go ahead and draw it because this one's nice to have a visual sense, even though you can just use math to compute it.

01:23 And i'm going to assume that the origin of my coordinate system is right in the middle of the cube.

01:29 And then the cube has sides of length 1 .4 meters.

01:35 Oh, that was a nice curly bracket.

01:38 Okay.

01:41 And so, yeah, and so let's draw the electric field.

01:50 And i'm going to do an even bigger cube because drawing on this tablet can get a little messy.

01:58 So let's figure out what this electric field looks like.

02:04 So i'm going to label these axes.

02:06 So here's x, here's y, here's z.

02:08 It's along the j -hat unit vector, so that means it's in the y direction.

02:13 And it seems to get bigger in magnitude the further you are from the origin.

02:18 So at the origin, it's zero.

02:20 I didn't even finish all my cube.

02:21 There we go.

02:23 But then it's kind of little, but it gets bigger and bigger and bigger, and the size increases linearly.

02:30 And for negative y, it's in the negative direction, and so it gets bigger and bigger and bigger.

02:37 And then it kind of extends up through here.

02:40 Maybe i'll use a different color to denote that.

02:52 So just to be totally clear, it extends up this way.

02:58 And then down and then in all the other directions.

03:00 So that would be a lot of arrows.

03:03 And so you can see already that it's not the situation you had before where the constant field where kind of what lines go in, go out.

03:11 All these lines are basically pointing out.

03:13 And so there's going to be some net flux.

03:17 But it's still the simple situation that it's constant along the face of each cube.

03:24 So to evaluate the total flux, then we need to evaluate the flux through each face.

03:32 So it's the integral over the surface of the whole cube.

03:42 But notice that only.

03:45 This right face and this left face have some flux because, like, for example, on the top face, the electric field is, oops, i guess not that way.

03:58 Oh, there's some lag.

03:59 Okay.

04:01 Yeah.

04:01 The field is to the right over here, for example, and then the area vector is like this.

04:07 And so, for example, right here, the dot product between these is zero or the angle between that.

04:14 Another way to say that is the cosine of the angle between them is 90 or the angle between them is 90 and the cosine of that is zero.

04:21 So this surface and this bottom surface, the front surface, the back surface have no flux through them.

04:27 So then it's just going to be the total flux is going to be the flux through the right plus the flux through the left.

04:38 So let's evaluate this...

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