Nlmo Analysis Essay
I’m posting this white paper “as is” but I will keep on coming back to update it; the thing is that I haven’t had the time to post anything else lately and if I don’t do it like this then I will never get it out. Please be kind on your comments and ratings!
For a more thorough discussion of NBO analysis please check out the references.
Requesting an NBO population analysis on the route section of a Gaussian job (via the simplest option pop=nbo) generates a lot of information on the output file which sometimes is not too straightforward to read. Please refer to previous posts in this blog (all under the NBO category) for more info on NBO calculations. The first part of this post deals with the analysis of the default information obtained from an NBO calculation; the second part deals with some useful/popular options of the NBO analysis which are controlled through the pop=nboread keyword available in NBO3.1 which is the version incorporated in Gaussian.
Perhaps the most common issue when reading NBO results is making sense of the hybridization shown. Take the example below as taken from the NBO manual for Methylamine:
(Occupancy) Bond orbital/ Coefficients/ Hybrids
1. (1.99858) BD (1) C 1 – N 2
(40.07%) 0.6330* C1 s(21.71%)p 3.61(78.29%)
-0.0003 -0.4653 -0.0238 -0.8808 -0.0291
-0.0786 -0.0110 -0.0000 -0.0000
(50.93%) 0.7742* N 2 s(30.88%)p 2.24(69.12%)
-0.0001 -0.5557 0.0011 0.8302 0.0004
0.0443 -0.0098 0.0000 0.0000
The first line shows the occupancy (between 0.00 and 2.00 electrons), then the label of the NBO (BD = Bonding (2 centers); CR = Core (1 center); LP = Lone pair; RY = Rydberg; BD* = Antibond), after that a ‘serial number‘ which corresponds to the connectivity (or idealized bond index between the atoms, i.e., single double triple bond), and finally the atom(s) to which the NBO belongs.
The next line describes the natural atomic hybrids of which the NBO is composed, giving the percentage (100|cA|^2) of the NBO on each hybrid (40% the C hybrid orbital and 60% the N hybrid orbital), the polarization coefficient cA (Nitrogen is more electronegative than Carbon, hence the polarization coefficients look like 0.633 for C and 0.7742 for N, i.e. this NBO is more polarized towards N), the atom label (self explanatory) , and a hybrid label showing the sp^x composition: for the C hybrid orbital it is sp^3.61 while for the one on N is sp^2.24. The number in parenthesis is just the percentage in composition of the hybrid (75%p and 25%s corresponds to an ideal sp^3 hybridization) Now, for the tricky part: Sometimes you’ll get numbers larger than 3 for an sp^x hybrid or even s^yp^x hybrids (for y>1 and x>3), this has to do with the basis set employed and the number of functions used to describe each atomic orbital. (EXAMPLE SOON, IM LAZY)
Below the hybridization we find the set of coefficients that specify how the NHO is written as a linear combination of Natural Atomic Orbitals. The previous NHO for C has the largest coefficients from the second (-0.4653) and fourth (-0.8808) natural atomic orbitals, corresponding to a rough description like: NHOc = -0.4653(2s)c -0.8808(2px)c
To control the options in the Natural Bond Orbital population analysis the line $NBO keywords $END must be included at the end of the input file (after the infamous blank line located after the molecule specification)
Wiberg bond indexes
This is a feature I use a lot when dealing with adducts with closed shell molecules. It is achieved through the BNDIDX keyword. Two indexes are obtained: The Wiberg bond index which is presented as a matrix; and the Wiberg bond index total which is the summation of all Wiberg indexes for every atom. The latter index roughly resembles the number of covalent bonds each atom forms. When analyzing this total index on a given atom, it should be compared to a well defined one in another part of the molecule just to make sure that all numbers are reflecting the same trends. Wiberg’s is not the only bond index provided by NBO analysis: the BOAO keyword generates bond index on the basis of the natural atomic orbitals.
Some common errors and possible solutions
->> Concerning NBO Deletion analysis
***** WARNING ***** The variational principle has been violated and the above deletion energy is invalid!!
This usually caused by one of the following:
1) Wavefunction symmetry breaking: Use the Nosymm option on the route section of your input file.
2) The use of DFT methods: Strong deletions often lead to densities that derail the density functional. Safest is to use HF, where the variational theorem can be counted on, and
DFT artifacts are averted. The FIXDM keyword (available only in NBO 5.0) may also correct some numerical problems associated with large basis sets
3) Deletion of some degenerated orbitals which breaks the symmetry of the wavefunction. Sometimes it could be that although there are no formal degenerate states accidental degeneracies might occur, deletion of which will cause this error.
->> Also on NBO Deletion Analysis
** ERROR IN INITNF. NUMBER OF VARIABLES ( 57) **
** INCORRECT (SHOULD BE BETWEEN 1 AND 50) **
This is one weird error. I have solved it by changing the molecule specification from Z-Matrix to Cartesian coordinates. Also, if you are running a DFT calculation in an older revision of Gaussian 03, try using the IOp(5/48=10000). Later revisions of Gaussian 03 and the more recent Gaussian 09 claim to have fixed this problem.
->> NBO Analysis
WARNING: Population inversion found on atom X#
This is not a problem! NBO lists orbitals within each atom according to their energy and their population afterwards. This warning only states that some low energy lying orbitals are less populated than others with higher energy. It cannot be “fixed” since this is a natural consequence of the orthonormalization process of the NBO generation.
NBO5.0 Home. Site of the creator of NBO and NBOView (Dr. Frank Weinhold)
FAQ‘s on NBO Home. I can’t recommend it enough!!!
Population Analysis Keyword in Gaussian
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Look for images or metaphors that the author uses consistently. What other sort of pattern can you identify in the text? How do you interpret this pattern so that your reader will understand the book, essay, poem, speech, etc. better?
What philosophical, moral, ethical, etc. ideas is the author advocating or opposing? What are the consequences of accepting the author's argument?
Explain how the work functions as a piece of rhetoric--how does the author attempt to convince his or her reader of something? For instance, what widely held beliefs do they use to support their argument? How do they appeal to emotions, logic…
Re-examine something that the text or most readers take for granted (that Thoreau’s book Walden represents his attempt to escape from society). Question this major premise and see where it takes you
Ask yourself if an author’s literary argument is inconsistent with itself or is in some way philosophically "dangerous," inadequate, unethical, or misleading.
Examine how characters are presented in a story. How do they help the main character to develop? Which characters are trustworthy? Which are not? Why are they presented this way?
Structure: How the parts of the book or essay follow one another; how the parts are assembled to make a whole? Why does the author start where they start, end where they end? What is the logical progression of thought? How might that progression be intended to affect the reader What effect might this progression of ideas have on a generic reader or on a reader from the time period in which the work was written? Does the piece move from the general to the specific or vice versa?
If you could divide the book/essay into sections, units of meaning, what would those sections be? How are they related to each other? Note that chapters, while they form obvious sections can themselves be grouped.
Referring to the text: In writing analytic papers that address any kind of literature, it is necessary to refer to the text (the specific words on the page of the book) in order to support your argument. This means that you must quote and interpret passages that demonstrate or support your argument. Quotation is usually stronger than paraphrase. Remember also that your purpose in writing an essay is not merely to paraphrase or summarize (repeat) what the author has said, but to make an argument about how the make their point, or how they have said what they have said.
Language: includes the way an author phrases his or her sentences, the key metaphors used (it’s up to you to explain how these metaphors are used, why these metaphors are appropriate, effective, ineffective, or ambiguous). Is the way a sentence is phrased particularly revealing of the author’s meaning?
Please title your paper and make the title apt and enticing--I LOVE a good title. It puts me in a good mood before I start reading.
Be clear about whether you’re writing about a book, an essay (non-fiction, short prose), a story (short fiction) a poem, a novel (book-length fiction), an autobiography, a narrative (as in Captivity Narratives) etc. Walden is a book comprised of chapters. Each of these chapters could also be called an essay. Within these essays, Thoreau sometimes tells stories. The book itself is not a story, but closer to a narrative, which is non-fiction.
Always go through at least two drafts of you paper. Let your paper sit, preferably for 24 hours between drafts sometime during the process of your writing.
Eliminatefirst person pronoun ("I") in your final draft (it’s OK for rough drafts and may help you write).
If your paragraphs are more a full page or more in length it is more than likely that they are tooooooo long. Probably you have too many ideas "in the air" at once. Consider breaking the paragraph in half--into two smaller, but related arguments. Your reader needs a break, needs more structure in order to be able to follow your meaning.
If several of your paragraphs are exceedingly short (4-5 lines), it is likely that you are not developing your ideas thoroughly enough--that you are writing notes rather than analysis. Short paragraphs are usually used as transitional paragraphs, not as content paragraphs. (Short paragraphs can be used in the rhetorical devise of reversal where you lead your reader down a certain path (to show them one side of the argument, the one you are going to oppose) and then turn away from that argument to state the true argument of your paper.)
Employ quotation often.One quotation per argumentative paragraph is usually necessary. Depending upon the length and complexity of the passage or topic you're dealing with, more quotations may be useful to prevent you from getting too far away from the text. Your quotations combined with your interpretations are your proof. Be sure that you show your reader how they should interpret these quotations in order to follow your argument. (Almost every quotation should be followed by an interpretation, a deeper reading of what is being said and how its being said. This interpretation demonstrates how the quotation supports the claim you're making about it). Pay attention to metaphor, phrasing, tone, alliteration, etc. How is the author saying what they are saying--what does that teach us about the text?
Remember to write directive (sometimes called "topic") sentences for your paragraphs. The first sentence of any paragraph should give your reader an idea of what the paragraph is going to say and how the paragraph will connect to the larger argument. It should have more to do with what you have to say about the materials than what the author him or herself has said.
Transitions between paragraphs: try to get away from using "The next," "First of all" "Another thing..." to connect your paragraphs. This is the "list" method of structuring a paper--not an integrated, logical approach. A really strong transition makes the logical connection between paragraphs or sections of a paper and gives the reader a sense that you’re building an argument. To make sure you are making a well-connected argument, ask yourself how the last sentence of each paragraph and the first sentence of the next are connected. Each of the sentences within your paragraphs should be related somehow (follow from, refer to, etc.) the one that precedes it, and the one which follows it. This will help the reader follow the flow of your ideas. The order of your paragraphs should reveal a developing argument.
On the most basic level, you should be able to consciously justify the presence and placement of every word in every sentence, every sentence in every paragraph, every paragraph in every essay. To repeat: in revising your papers after the first draft (which is always, inevitably to some degree confused because you are involved in the process of working your ideas out), you should be highly conscious of what you are doing and why you are doing it.