This table is a relatively clean listing of the NBOs along with their occupancies and energies. The Principle delocalizations column lists the other orbitals with which each NBO interacts most strongly; the Second Order Perturbation Theory Analysis table can provide more details on these (see the previous annotation).

One of the most powerful aspects of NBO theory is its ability to reveal interactions between bonding and antibonding orbitals, highlighting parts of a molecule where resonance might be relevant due to electron delocalization effects. When filled and empty NBOs overlap in space, a "flow" of electrons from the filled to the empty NBO can occur that stabilizes both NBOs. Such "flow" is relevant to both resonance within a molecule and reactivity between molecules.

This table lists relatively strong (>0.5 kcal/mol stabilization) interactions between filled (Donor) NBOs and empty (Acceptor) NBOs. The donor orbital is always BD or LP while the acceptor is always BD, LP, or RY (Rydberg). We can often draw a resonance structure and resonance-type electron flow to depict these interactions using the Lewis formalism. For an example, check out the interaction between NBO 1 and NBO 74, which provides a remarkable 11 kcal/mol of stabilization. This is a (\sigma \rightarrow \pi^) interaction between the Si1–C2 sigma bonding NBO and the C3–C4 pi antibonding NBO. We can represent it using resonance structures and curved arrows as follows:

This resonance form suggests that C4 (the terminal carbon) ought to be more negatively charged than C3. Lo and behold, if you scroll back up to the Natural Population Analysis, you'll see that this is the case...by a large margin! C4 has a partial charge of –0.25 while the partial charge of C3 is only –0.03.

This example shows us how we can use NBOs and interactions between them to begin to make arguments and draw conclusions about structure and reactivity. It's an incredibly useful theoretical framework for thinking about molecules!

Finally, this is a pi antibonding orbital. Note the coefficients with opposite sign, the nearly pure p nature of the NHOs, and the slight polarization toward carbon 3.

I encourage you to explore the other NBOs, either by perusing this table or running a calculation yourself on the WebMO demo server. For example, can you find the sp hybrid orbitals and the C3–C4 sigma bonding and antibonding NBOs in the table?

Here we have our first antibonding orbital (BD*). Three important things to notice here that will be true of all antibonding NBOs:

1. The NHOs used to build this NBO are identical to those used to build NBO 1.
2. The coefficients are opposite in sign, indicating that there will be diminished density and a node between the nuclei perpendicular to the bonding axis.
3. The occupancy is quite low, but not zero.

The first two points get at the idea that bonding orbitals are "NHO1 + NHO2" and antibonding orbitals are "NHO1 – NHO2"; this will always be true as bonding and antibonding orbitals must be orthogonal.

On the third point, occupation of antibonding orbitals points to electron delocalization or resonance effects. You can think of this as "leakage" from overlapping bonding NBOs into antibonding NBOs. More on this below.

This is the other pi bonding NBO for the triple bond. It is a bit different from NBO 9...that seems odd! Notice though that this orbital is oriented differently—especially with respect to the C2–Si1 bond—than NBO 9. NBO 10 is perpendicular to this bond (see below) while NBO 9 is parallel to it (see the last annotation).

Because it interacts differently with this bond, its energy and composition are slightly different. Most notably, it is polarized in the opposite direction: more electron density is on C3 than C4 in this orbital.

NBO 9 is one of two pi bonding NBOs for the C3–C4 triple bond (NBO 10 is the other). Notice that the "hybridization" of each NHO is essentially pure p although they do have a miniscule amount of s character. The percentages and coefficients show that the bond is ever-so-slightly polarized toward C4.

This is the sigma bonding orbital for the Si1–H8 bond. Notice that the NHO on silicon does not match the NHO used to make NBO 1—fractional hybridization also allows the hybrid orbitals used for each orbital to differ. However, if you examine the antibonding orbital for this bond (NBO 67) you'll notice that the exact same NHO is used; this is always the case. More on antibonding orbitals below.

Is the bond polarized toward hydrogen or silicon? Which atom has more electron density in the bond?

These numbers are related to construction of the NBO from the NHOs. They answer the questions:

1. What percentage of the NBO is this NHO?
2. What is the coefficient of this NHO in the mathematical representation of the NBO?
3. What atom does this NHO live on?

Here, the \(sp^{2.88}d^{0.07}\) NHO on silicon is 26.30% of NBO 1. Examining the other NHO used to build this NBO, we see that it is naturally the remaining 73.70% of the NBO. These percentages are derived from squaring the coefficients and normalizing the sum of the squares to 100 (try it yourself!).

All in all, the shape of the orbital and these hybrid orbitals indicate that this is the sigma bonding orbital for the Si1–C2 bond (see below). Next, we'll examine a few more NBOs of significance in this molecule.

What's all this? The leading "1" indicates that this is a description of NHO 1. There are always either one (LP, LP, Cor, Ryd) or two (BD, BD) NHO contributors to each NBO.

You can read the rest as a description of the NHO in terms of atomic orbitals: \(sp^{2.88}d^{0.07}\). Once again we find something odd: fractional hybridization is allowed! Hybrid orbitals are just mixed versions of the atomic orbitals and the complicated truth is we can mix them in whatever proportions work best to represent the molecular wavefunction.

These will usually be very close to your basic expectations, but deviations can point to interesting phenomena, especially deviations from VSEPR geometry and bond polarization.

This list of 19 numbers looks extremely cryptic. What are they? Why 19? Roll back up to the listing of NAOs ("NATURAL POPULATIONS"). How many NAOs does silicon have? Of course, 19! These 19 numbers list the coefficient on each silicon NAO used to build the natural hybrid orbital (NHO) on silicon for this natural bond orbital (NBO).

Each carbon NHO will have 15 coefficients and each hydrogen will have only 2. Why?

For this particular NBO, notice that the hybridization of silicon is essentially \(sp^3\) and that the big NAO contributors are the 3s and 3p orbitals. You usually don't need to look at this listing; you can go right to the hybridization on the line above. Head there now.

This is the occupancy of the orbital, but remember to think about it as an electron density. This value answers the question: treating the total number of electrons in the molecule as the total density, how much electron density is in this orbital?

The spacing makes this label hard to read but it's super helpful! "BD" without an asterisk indicates a bonding orbital. "(1)" indicates a sigma orbital; "(2)" and "(3)" indicate pi orbitals (and you can and should check this by examining the orbital shapes). "Si1 – C2" tells us this orbital lives in the bond between silicon 1 and carbon 2.

Next, move down to the rectangular list of 19 numbers two lines down.

This percentage is worth glancing at; colloquially it answers the question "how close is our Lewis structure to reality?"

The table below this one lists the NBOs (numbered on the far left) and their constituent hybrid orbitals, representing each as a set of coefficients. Let's walk through it one step at a time.

"Starting at the end," the table above tells us that the vast majority of the electron density is living in NBOs that can be directly associated with the Lewis structure: \(\sigma\), \(\sigma^*\), \(\pi\), \(\pi^*\), n, and a. The NBO program calls n orbitals "LP" (lone pair) and a orbitals "LP*" (a lone pair would be here, but it's empty).

Non-Lewis electron density is occupying Rydberg orbitals. This is necessary to faithfully represent the full molecular wavefunction but is only a problem if the Rydberg density is large (in which case, our Lewis structure is a bad representation of the quantum model).

This is where things get really exciting. Natural hybrid orbitals (NHOs) are constructed from the NAOs and natural bond orbitals (NBOs) are constructed from the NHOs.

These numbers should be close to your expectations from introductory chemistry and the periodic table but will differ. Check out C2: 4.9 valence electrons at carbon?! This reflects the polarization of bonds and electronegativity. Because carbon is the most electronegative atom in the molecule (check it!), it pulls a good bit of electron density toward itself.

There is no single "correct" way to determine the charge "at" or "on" an atom in a molecule, since an atom in a molecule has no rigorously defined boundary. The way NBO theory does it is to sum all of the electron densities in all of the NAOs associated with an atom and subtract that from Z, the atomic number. The Natural Charge column lists that value for each atom in the molecule.

Why the warning? Electron density below 2.0 in the core shells indicates that core electron density is participating in bonding to some extent (this isn't normal: only valence electrons engage in bonding). This is usually not a big deal at all though; here for example, the problematic density is 1.998—still darn close to 2.0!

The Energy column lists the energy of each NAO in kcal/mol; this is related to how stable electrons are in that orbital.

The Occupancy column lists the number of electrons in each NAO and we immediately recognize something strange: NBO theory allows fractional occupancies! You can think of this value as a measure of the electron density in the orbital; 2.0 is the maximum due to the Pauli exclusion principle.

Check out the Type(AO) column for the subshell label (e.g., 2s) and whether the NAO is in in a core shell (Cor), valence shell (Val), or Rydberg shell (Ryd). Rydberg shells are empty shells that are not used in conventional bonding descriptions (in other words, they're not even used to construct antibonding orbitals except to a negligible degree).

You don't need to pay a ton of attention to the lang column although it lists the specific orbital (i.e. specific directionality and shape) corresponding to each NAO.

The No column refers to the number of the atom on which each NAO originates. For example, a molecule with two carbons will contain C1 and C2; this column would list "1" for NAOs on C1 and "2" for NAOs on C2. Nothing too fancy!

The Atom column indicates the atom on which each NAO originates.

The table below summarizes the natural atomic orbitals (NAOs), which closely resemble the 1s, 2s, 2p, etc. atomic orbitals you've seen before.

Welcome to the NBO results for propargyl silane! Atom numbering in the molecule is as shown below. Silicon is atom 1; that's tough to see. Most important is that carbons 3 and 4 are triply bonded and carbon 3 is the internal carbon.

Every Gaussian calculation comes with a quotation. Now you know.

Howdy! This monstrous text file is the output of a natural bond orbital (NBO) calculation on the molecule propargyl silane, \(\mathrm{H_3SiCH_2CCH}\). Although this is a fairly big molecule, it's a nice one to introduce NBO theory because it includes sigma and pi orbitals and some important (and not necessarily obvious) orbital interactions.

Using Control- or Command-F, skip all the way down to the "Gaussian NBO Version 3.1" section to begin.

What's all this? The leading "1" indicates that this is a description of NHO 1. There are always either one (LP, LP, Cor, Ryd) or two (BD, BD) NHO contributors to each NBO.

You can read the rest as a description of the NHO in terms of atomic orbitals: \(sp^{2.88}d^{0.07}\). Once again we find something odd: fractional hybridization is allowed! Hybrid orbitals are just mixed versions of the atomic orbitals and the complicated truth is we can mix them in whatever proportions work best to represent the molecular wavefunction.

These will usually be very close to your basic expectations, but deviations can point to interesting phenomena, especially deviations from VSEPR geometry and bond polarization.

Every Gaussian calculation comes with a quotation. Now you know.

One of the most powerful aspects of NBO theory is its ability to reveal interactions between bonding and antibonding orbitals, highlighting parts of a molecule where resonance might be relevant due to electron delocalization effects. When filled and empty NBOs overlap in space, a "flow" of electrons from the filled to the empty NBO can occur that stabilizes both NBOs. Such "flow" is relevant to both resonance within a molecule and reactivity between molecules.

This table lists relatively strong (>0.5 kcal/mol stabilization) interactions between filled (Donor) NBOs and empty (Acceptor) NBOs. The donor orbital is always BD or LP while the acceptor is always BD, LP, or RY (Rydberg). We can often draw a resonance structure and resonance-type electron flow to depict these interactions using the Lewis formalism. For an example, check out the interaction between NBO 1 and NBO 74, which provides a remarkable 11 kcal/mol of stabilization. This is a (\sigma \rightarrow \pi^) interaction between the Si1–C2 sigma bonding NBO and the C3–C4 pi antibonding NBO. We can represent it using resonance structures and curved arrows as follows:

This resonance form suggests that C4 (the terminal carbon) ought to be more negatively charged than C3. Lo and behold, if you scroll back up to the Natural Population Analysis, you'll see that this is the case...by a large margin! C4 has a partial charge of –0.25 while the partial charge of C3 is only –0.03.

This example shows us how we can use NBOs and interactions between them to begin to make arguments and draw conclusions about structure and reactivity. It's an incredibly useful theoretical framework for thinking about molecules!

This table is a relatively clean listing of the NBOs along with their occupancies and energies. The Principle delocalizations column lists the other orbitals with which each NBO interacts most strongly; the Second Order Perturbation Theory Analysis table can provide more details on these (see the previous annotation).

Finally, this is a pi antibonding orbital. Note the coefficients with opposite sign, the nearly pure p nature of the NHOs, and the slight polarization toward carbon 3.

I encourage you to explore the other NBOs, either by perusing this table or running a calculation yourself on the WebMO demo server. For example, can you find the sp hybrid orbitals and the C3–C4 sigma bonding and antibonding NBOs in the table?

Howdy! This monstrous text file is the output of a natural bond orbital (NBO) calculation on the molecule propargyl silane, \(\mathrm{H_3SiCH_2CCH}\). Although this is a fairly big molecule, it's a nice one to introduce NBO theory because it includes sigma and pi orbitals and some important (and not necessarily obvious) orbital interactions.

Using Control- or Command-F, skip all the way down to the "Gaussian NBO Version 3.1" section to begin.

Here we have our first antibonding orbital (BD*). Three important things to notice here that will be true of all antibonding NBOs:

1. The NHOs used to build this NBO are identical to those used to build NBO 1.
2. The coefficients are opposite in sign, indicating that there will be diminished density and a node between the nuclei perpendicular to the bonding axis.
3. The occupancy is quite low, but not zero.

The first two points get at the idea that bonding orbitals are "NHO1 + NHO2" and antibonding orbitals are "NHO1 – NHO2"; this will always be true as bonding and antibonding orbitals must be orthogonal.

On the third point, occupation of antibonding orbitals points to electron delocalization or resonance effects. You can think of this as "leakage" from overlapping bonding NBOs into antibonding NBOs. More on this below.

This is the other pi bonding NBO for the triple bond. It is a bit different from NBO 9...that seems odd! Notice though that this orbital is oriented differently—especially with respect to the C2–Si1 bond—than NBO 9. NBO 10 is perpendicular to this bond (see below) while NBO 9 is parallel to it (see the last annotation).

Because it interacts differently with this bond, its energy and composition are slightly different. Most notably, it is polarized in the opposite direction: more electron density is on C3 than C4 in this orbital.

NBO 9 is one of two pi bonding NBOs for the C3–C4 triple bond (NBO 10 is the other). Notice that the "hybridization" of each NHO is essentially pure p although they do have a miniscule amount of s character. The percentages and coefficients show that the bond is ever-so-slightly polarized toward C4.

This list of 19 numbers looks extremely cryptic. What are they? Why 19? Roll back up to the listing of NAOs ("NATURAL POPULATIONS"). How many NAOs does silicon have? Of course, 19! These 19 numbers list the coefficient on each silicon NAO used to build the natural hybrid orbital (NHO) on silicon for this natural bond orbital (NBO).

Each carbon NHO will have 15 coefficients and each hydrogen will have only 2. Why?

For this particular NBO, notice that the hybridization of silicon is essentially \(sp^3\) and that the big NAO contributors are the 3s and 3p orbitals. You usually don't need to look at this listing; you can go right to the hybridization on the line above. Head there now.

This is the sigma bonding orbital for the Si1–H8 bond. Notice that the NHO on silicon does not match the NHO used to make NBO 1—fractional hybridization also allows the hybrid orbitals used for each orbital to differ. However, if you examine the antibonding orbital for this bond (NBO 67) you'll notice that the exact same NHO is used; this is always the case. More on antibonding orbitals below.

Is the bond polarized toward hydrogen or silicon? Which atom has more electron density in the bond?

These numbers are related to construction of the NBO from the NHOs. They answer the questions:

1. What percentage of the NBO is this NHO?
2. What is the coefficient of this NHO in the mathematical representation of the NBO?
3. What atom does this NHO live on?

Here, the \(sp^{2.88}d^{0.07}\) NHO on silicon is 26.30% of NBO 1. Examining the other NHO used to build this NBO, we see that it is naturally the remaining 73.70% of the NBO. These percentages are derived from squaring the coefficients and normalizing the sum of the squares to 100 (try it yourself!).

All in all, the shape of the orbital and these hybrid orbitals indicate that this is the sigma bonding orbital for the Si1–C2 bond (see below). Next, we'll examine a few more NBOs of significance in this molecule.

The spacing makes this label hard to read but it's super helpful! "BD" without an asterisk indicates a bonding orbital. "(1)" indicates a sigma orbital; "(2)" and "(3)" indicate pi orbitals (and you can and should check this by examining the orbital shapes). "Si1 – C2" tells us this orbital lives in the bond between silicon 1 and carbon 2.

Next, move down to the rectangular list of 19 numbers two lines down.

This is the occupancy of the orbital, but remember to think about it as an electron density. This value answers the question: treating the total number of electrons in the molecule as the total density, how much electron density is in this orbital?

This percentage is worth glancing at; colloquially it answers the question "how close is our Lewis structure to reality?"

The table below this one lists the NBOs (numbered on the far left) and their constituent hybrid orbitals, representing each as a set of coefficients. Let's walk through it one step at a time.

"Starting at the end," the table above tells us that the vast majority of the electron density is living in NBOs that can be directly associated with the Lewis structure: \(\sigma\), \(\sigma^*\), \(\pi\), \(\pi^*\), n, and a. The NBO program calls n orbitals "LP" (lone pair) and a orbitals "LP*" (a lone pair would be here, but it's empty).

Non-Lewis electron density is occupying Rydberg orbitals. This is necessary to faithfully represent the full molecular wavefunction but is only a problem if the Rydberg density is large (in which case, our Lewis structure is a bad representation of the quantum model).

This is where things get really exciting. Natural hybrid orbitals (NHOs) are constructed from the NAOs and natural bond orbitals (NBOs) are constructed from the NHOs.

Welcome to the NBO results for propargyl silane! Atom numbering in the molecule is as shown below. Silicon is atom 1; that's tough to see. Most important is that carbons 3 and 4 are triply bonded and carbon 3 is the internal carbon.

These numbers should be close to your expectations from introductory chemistry and the periodic table but will differ. Check out C2: 4.9 valence electrons at carbon?! This reflects the polarization of bonds and electronegativity. Because carbon is the most electronegative atom in the molecule (check it!), it pulls a good bit of electron density toward itself.

There is no single "correct" way to determine the charge "at" or "on" an atom in a molecule, since an atom in a molecule has no rigorously defined boundary. The way NBO theory does it is to sum all of the electron densities in all of the NAOs associated with an atom and subtract that from Z, the atomic number. The Natural Charge column lists that value for each atom in the molecule.

Why the warning? Electron density below 2.0 in the core shells indicates that core electron density is participating in bonding to some extent (this isn't normal: only valence electrons engage in bonding). This is usually not a big deal at all though; here for example, the problematic density is 1.998—still darn close to 2.0!

You don't need to pay a ton of attention to the lang column although it lists the specific orbital (i.e. specific directionality and shape) corresponding to each NAO.

The No column refers to the number of the atom on which each NAO originates. For example, a molecule with two carbons will contain C1 and C2; this column would list "1" for NAOs on C1 and "2" for NAOs on C2. Nothing too fancy!

The Atom column indicates the atom on which each NAO originates.

The Occupancy column lists the number of electrons in each NAO and we immediately recognize something strange: NBO theory allows fractional occupancies! You can think of this value as a measure of the electron density in the orbital; 2.0 is the maximum due to the Pauli exclusion principle.

The table below summarizes the natural atomic orbitals (NAOs), which closely resemble the 1s, 2s, 2p, etc. atomic orbitals you've seen before.

The Energy column lists the energy of each NAO in kcal/mol; this is related to how stable electrons are in that orbital.

Check out the Type(AO) column for the subshell label (e.g., 2s) and whether the NAO is in in a core shell (Cor), valence shell (Val), or Rydberg shell (Ryd). Rydberg shells are empty shells that are not used in conventional bonding descriptions (in other words, they're not even used to construct antibonding orbitals except to a negligible degree).

Link references in context using a format like this: (Author(s) Year). Use "et al." for more than two authors. Don't overdo citations; try to ensure your post remains readable and flows well. You do not need to include a References section at the end of the post.

As you read through this post, look for places where concepts and analytical skills from CHEM 1315 are invoked. The post is a mixture of self-analysis (e.g., the sections on acid-base equilibrium and curved arrows for the decarboxylation of sorbic acid) and literature summaries (e.g., the section on human health effects).

As a summative assignment for CHEM 1315, your blog post should show me what you know and what you can do as a result of your learning in the course. You'll find yourself forced to summarize some things because of gaps or incomplete understanding in the literature. That's okay—but your post should be more than a summary. Show me what you're capable of!

This should probably be linked to Wikipedia.

Much of this section is a summary of the work described in the linked papers. In all honesty, the work doesn't get to the level of bonds and atoms that we'd like to see in an organic chemistry course. However, given the importance of the associated signature question and the studies that have been done, summarizing and then saying "little is known" is fine.

Note the structural analogy!

These curved arrows suggest a concerted mechanism, which may or may not occur in practice. When/if you come across a mechanistic study, gather as many details as you can to build as precise a picture as you can. Lacking details however, any chemically reasonable and logical mechanism is okay. In enzymatic mechanisms, the specific acids and bases involved are often not known (they're amino acid side chains). Using generic acids and bases HA and B is fine. For solution reactions involving aqueous acid and base, use hydronium and hydroxide.

Recognizing the class of this organic reaction. We will regularly classify reactions as substitutions, additions, eliminations, or rearrangements throughout the course.

Polarity and intermolecular forces are relevant here.

Note the deep understanding of the dynamic nature of chemical equilibrium conveyed by this paragraph.

Chemical equilibrium (thermodynamics): an important way of seeing in CHEM 1315! See also the figure below.

Include PubChem links for any compound names and Wikipedia links (or other reputable sources) for jargon—especially jargon outside of the scope of CHEM 1315. The IUPAC Gold Book is a great source for chemistry terms.

I included numbers in the section headings so that the sections can be related back to the signature questions. While not required by any means, I like the way this allows the reader to refer back to the signature questions.

Structural stability factors again.

Stability factors! If I had more time, I would've included a figure displaying the resonance forms of benzoate with curved arrows illustrating their interconversion.

Your signature questions should appear somewhere in the introduction to the post.

Functional groups: an important way of seeing organic Lewis structures in CHEM 1315! This helps the reader conceptualize the molecule and makes it clear that the author knows what he's talking about.

Biochemical studies very often don't get to the level of bonds, atoms, and "pushing electrons." You'll want to try to get as close as you can, using what's known and making inferences from published work, but it's okay if you can't get all the way to a curved-arrow mechanism for a biochemical effect. Your post should include at least one mechanism with curved arrows.

Although not directly covered in CHEM 1315, concentration is a fundamental concept from introductory chemistry. It's also a useful metric to frame a discussion of health effects, flavor, efficacy, and mechanisms.

Acidity and basicity are an important theme in this post. Notice how the post demonstrates a strong understanding of acid-base equilibria and structural features that reflect acidity.

Consistent with the idea from rhodium catalysis that transmetalation of the arylboronic acid to the metal is the turnover-limiting step.

Rhodium catalysts are common for this type of chemistry. E.g., see Org. React. 2017, 93, 1.