# Blog Archives

## Population Analysis in the Excited State with Gaussian

To calculate what the bonding properties of a molecule are in a particular excited state we can run any population analysis following the root of interest. This straightforward procedure takes two consecutive calculations since you don’t necessarily know before hand which excited state is the one of interest.

The regular Time Dependent Density Functional Theory (TD-DFT) calculation input with Gaussian 16 looks as follows (G09 works pretty much the same), let us assume we’ve already optimized the geometry of a given molecule:

%OldChk=filename.chk %nprocshared=16 %chk=filename_ES.chk #p TD(NStates=10,singlets) wb97xd/cc-pvtz geom=check guess=read Title Card Required 0 1 --blank line--

This input file retrieves the geometry and wavefunction from a previous calculation from filename.chk and doesn’t write anything new into it (that is what `%OldChk=filename.chk` means) and creates a new checkpoint where the excited states are calculated (`%chk=filename_ES.chk`)

In the output you search for the transition which peeks your interest; most often than not you’ll be interested in the one with the highest oscillator strength, *f*. The oscillator strength is a dimensionless number that represents the ratio of the observed, integrated, absorption coefficient to that calculated for a single electron in a three-dimensional harmonic potential [Harris & Bertolucci, Symmetry and Spectroscopy]; in other words, it is related to the probability of that transition to occur, and therefore it takes values from 0.0 to 1.0 (for single photon absorption processes.)

The output of this calculation looks as follows, the value of f for every excitation is reported together with its energy and the orbital transitions which comprise it.

Excitation energies and oscillator strengths: Excited State 1: Singlet-A 3.1085 eV 398.86 nm f=0.0043 <S**2>=0.000 56 -> 59 -0.11230 58 -> 59 0.69339 This state for optimization and/or second-order correction. Total Energy, E(TD-HF/TD-DFT) = -1187.56377917 Copying the excited state density for this state as the 1-particle RhoCI density. Excited State 2: Singlet-A 4.0827 eV 303.68 nm f=0.0016 <S**2>=0.000 52 -> 59 0.46689 52 -> 64 -0.20488 53 -> 59 0.19693 54 -> 59 0.40414 54 -> 64 -0.16261 ... ... Excited State 8: Singlet-A 5.2345 eV 236.86 nm f=0.8063 <S**2>=0.000 52 -> 60 0.17162 53 -> 59 0.47226 53 -> 60 -0.11771 54 -> 59 -0.27658 54 -> 60 -0.22006 55 -> 59 0.20496 56 -> 59 0.15029

Now we’ve selected excited state #8 because it has the largest value of f from the lot, we use the following input to read in the geometry from the old checkpoint file and we generate a new one in case we need it for something else. The input file for doing all this looks as follows (I’ve selected as usual the Natural Bond Orbital population analysis):

%oldchk=a_ES.chk %nprocshared=16 %chk=a_nbo.chk #p TD(Read,Root=8) wb97xd/cc-pvtz geom=check density=current guess=read pop=NBORead Title Card Required 0 1 $NBO BOAO BNDIDX E2PERT $END --blank line--

The flags at the bottom request the calculation of Wiberg Bond Indexes (BNDIDX) as well as Bond Order in the Atomic Orbital basis (BOAO) and a second order perturbation theory for the electronic delocalization (E2PERT). Now we can compare the population analysis between ground and the 8th excited state; check figure 1 and notice the differences in Wiberg’s bond order for this complex made of two molecules and one Na+ cation.

In this example we can observe that in the ground state we have a neutral and a negative molecule together with a Na+ cation, but when we analyze the population in the 8th excited state both molecules acquire a similar charge, ca. **0.46 e**, which means that some of the electron density has been transferred from the negative one to the neutral molecule, forming an

*Electron Donor-Acceptor*complex (EDA) in the excited state.

This procedure can be extended to any other kind of population analysis and their derived combination, e.g. one could calculate their condensed fukui functions in the Nth excited state; but beware! These calculations yield vertical excitations, should the excited state of interest have a minimum we can first optimize the ES geometry and then perform the population analysis on said geometry; just add the opt keyword to perform both jobs in one go, but bear in mind that the NBO population analysis is performed before and after the optimization process so look for the tables and values closer to the end of the output file.

In the case of open shell systems the procedure is the same but one should be extremely careful in searching for the total population analysis since the output file contains this table for the alpha and beta populations separately as well as the added values for the total number of electrons.

## Percentage of Molecular Orbital Composition – G09,G16

Canonical Molecular Orbitals are–by construction–delocalized over the various atoms making up a molecule. In some contexts it is important to know how much of any given orbital is made up by a particular atom or group of atoms, and while you could calculate it by hand given the coefficients of each MO in terms of every AO (or basis set function) centered on each atom there is a straightforward way to do it in Gaussian.

If we’re talking about ‘dividing’ a molecular orbital into atomic components, we’re most definitely talking about population analysis calculations, so we’ll resort to the ** pop** keyword and the

**option in the standard syntax:**

`orbitals`#p M052x/cc-pVDZ pop=orbitals

This will produce the following output right after the Mulliken population analysis section:

Atomic contributions to Alpha molecular orbitals: Alpha occ 140 OE=-0.314 is Pt1-d=0.23 C38-p=0.16 C31-p=0.16 C36-p=0.16 C33-p=0.15 Alpha occ 141 OE=-0.313 is Pt1-d=0.41 Alpha occ 142 OE=-0.308 is Cl2-p=0.25 Alpha occ 143 OE=-0.302 is Cl2-p=0.72 Pt1-d=0.18 Alpha occ 144 OE=-0.299 is Cl2-p=0.11 Alpha occ 145 OE=-0.298 is C65-p=0.11 C58-p=0.11 C35-p=0.11 C30-p=0.11 Alpha occ 146 OE=-0.293 is C58-p=0.10 Alpha occ 147 OE=-0.291 is C22-p=0.09 Alpha occ 148 OE=-0.273 is Pt1-d=0.18 C11-p=0.12 C7-p=0.11 Alpha occ 149 OE=-0.273 is Pt1-d=0.18 Alpha vir 150 OE=-0.042 is C9-p=0.18 C13-p=0.18 Alpha vir 151 OE=-0.028 is C7-p=0.25 C16-p=0.11 C44-p=0.11 Alpha vir 152 OE=0.017 is Pt1-p=0.10 Alpha vir 153 OE=0.021 is C36-p=0.15 C31-p=0.14 C63-p=0.12 C59-p=0.12 C38-p=0.11 C33-p=0.11 Alpha vir 154 OE=0.023 is C36-p=0.13 C31-p=0.13 C63-p=0.11 C59-p=0.11 Alpha vir 155 OE=0.027 is C65-p=0.11 C58-p=0.10 Alpha vir 156 OE=0.029 is C35-p=0.14 C30-p=0.14 C65-p=0.12 C58-p=0.11 Alpha vir 157 OE=0.032 is C52-p=0.09 Alpha vir 158 OE=0.040 is C50-p=0.14 C22-p=0.13 C45-p=0.12 C17-p=0.11 Alpha vir 159 OE=0.044 is C20-p=0.15 C48-p=0.14 C26-p=0.12 C54-p=0.11

Alpha and Beta densities are listed separately only in unrestricted calculations, otherwise only the first is printed. Each orbital is listed sequentially (occ = occupied; vir = virtual) with their energy value (OE = orbital energy) in atomic units following and then the fraction with which each atom contributes to each MO.

By default only the ten highest occupied orbitals and ten lowest virtual orbitals will be assessed, but the number of MOs to be analyzed can be modified with ** orbitals=N**, if you want to have all orbitals analyzed then use the option

**instead of just**

`AllOrbitals``. Also, the threshold used for printing the composition is set to 10% but it can be modified with the option`

**orbitals**`, for the same compound as before here’s the output lines for HOMO and LUMO (MOs 149, 150) with ThreshOrbitals set to N=1, i.e. 1% as occupation threshold (`

**ThreshOrbitals=N**`):`

**ThreshOrbitals=1**Alpha occ 149 OE=-0.273 is Pt1-d=0.18 N4-p=0.08 N6-p=0.08 C20-p=0.06 C13-p=0.06 C48-p=0.06 C9-p=0.06 C24-p=0.05 C52-p=0.05 C16-p=0.04 C44-p=0.04 C8-p=0.03 C15-p=0.03 C17-p=0.03 C45-p=0.02 C46-p=0.02 C18-p=0.02 C26-p=0.02 C54-p=0.02 N5-p=0.01 N3-p=0.01 Alpha vir 150 OE=-0.042 is C9-p=0.18 C13-p=0.18 C44-p=0.08 C16-p=0.08 C15-p=0.06 C8-p=0.06 N6-p=0.04 N4-p=0.04 C52-p=0.04 C24-p=0.04 N5-p=0.03 N3-p=0.03 C46-p=0.03 C18-p=0.03 C48-p=0.02 C20-p=0.02

The ` fragment=n` label in the coordinates can be used as in BSSE Counterpoise calculations and the output will show the orbital composition by fragments with the label

`"Fr"`, grouping all contributions to the MO by the AOs centered on the atoms in that fragment.

As always, thanks for reading, sharing, and rating. I hope someone finds this useful.

## Fixing the error: Bad data into FinFrg

I found this error in the calculation of two interacting fragments, both with unpaired electrons. So, two radicals interact at a certain distance and the full system is deemed as a singlet, therefore the unpaired electron on each fragment have opposite spins. The problem came when trying to calculate the Basis Set Superposition Error (BSSE) because in the Counterpoise method you need to assign a charge and multiplicity to each fragment, however it’s not obvious how to assign opposite spins.

The core of the problem is related to the *guess *construction; normally a Counterpoise calculation would look like the following example:

#p B3LYP/6-31G(d,p) counterpoise=2 -2,1 -1,2 -1,2 C(Fragment=1) 0.00 0.00 0.00 O(Fragment=2) 1.00 1.00 1.00 ...

In which the first pair of charge-multiplicity numbers correspond to the whole molecule and the following to those of each fragment in increasing order of *N* (in this case, *N* = 2). So for this hypothetical example we have two anions (but could easily be two cations) each with an unpaired electron, yielding a complex of charge = -2 and a singlet multiplicity which implies those two unpaired electrons have opposite spin. But if the *guess *(the initial trial wavefunction from which the SCF will begin) has a problem understanding this then the title error shows up:

Bad data into FinFrg Error termination via Lnk1e ...

The solution to this problem is as simple as it may be obscure: Create a convenient guess wavefunction by placing a negative sign to the multiplicity of one of the fragments in the following example. You may then use the guess as the starting point of other calculations since it will be stored in the checkpoint file. By using this negative sign we’re not requesting a *negative multiplicity*, but a given multiplicity of *opposite spin *to the other fragment.

#p B3LYP/6-31G(d,p) guess=(only,fragment=2) -2,1 -1,2 -1,-2 C(Fragment=1) 0.00 0.00 0.00 O(Fragment=2) 1.00 1.00 1.00 ...

This way, the second fragment will have the opposite spin (but the same *multiplicity*) as the first fragment. The only keyword tells gaussian to only calculate the guess wave function and then exit the program. You may then use that guess as the starting point for other calculations such as my failed Counterpoise one.

## Density Keyword in Excited State Calculations with Gaussian

I have written about extracting information from excited state calculations but an important consideration when analyzing the results is the proper use of the keyword *density*.

This keyword let’s Gaussian know which density is to be used in calculating some results. An important property to be calculated when dealing with excited states is the change in dipole moment between the ground state and any given state. The Transition Dipole Moment is an important quantity that allows us to predict whether any given electronic transition will be allowed or not. A change in the dipole moment (i.e. non-zero) of a molecule during an electronic transition helps us characterize said transition.

Say you perform a TD-DFT calculation without the *density* keyword, the default will provide results on the lowest excited state from all the requested states, which may or may not be the state of interest to the transition of interest; you may be interested in the dipole moment of all your excited states.

Three separate calculations would be required to calculate the change of dipole moment upon an electronic transition:

1) A regular DFT for the ground state as a reference

2) TD-DFT, to calculate the electronic transitions; request as many states as you need/want, analyze it and from there you can see which transition is the most important.

3) Request the density of the Nth state of interest to be recovered from the checkpoint file with the following route section:

# TD(Read,Root=N)LOTDensity=Current Guess=Read Geom=AllCheck

replace *N* for the *N*th state which caught your eye in step number 2) and *LOT* for the *Level of Theory* you’ve been using in the previous steps. That should give you the dipole moment for the structure of the *N*th excited state and you can compare it with the one in the ground state calculated in 1). Again, if density=current is not used, only properties of *N*=1 will be printed.

## Calculating NMR shifts – Short and Long Ways

Nuclear Magnetic Resonance is a most powerful tool for elucidating the structure of diamagnetic compounds, which makes it practically universal for the study of organic chemistry, therefore the calculation of ^{1}H and ^{13}C chemical shifts, as well as coupling constants, is extremely helpful in the assignment of measured signals on a spectrum to an actual functional group.

Several packages offer an additive (group contribution) empirical approach to the calculation of chemical shifts (ChemDraw, Isis, ChemSketch, etc.) but they are usually only partially accurate for the simplest molecules and no insight is provided for the more interesting effects of long distance interactions (*vide infra*) so quantum mechanical calculations are really the way to go.

With Gaussian the calculation is fairly simple just use the NMR keyword in the route section in order to calculate the NMR shielding tensors for relevant nuclei. Bear in mind that an optimized structure with a large basis set is required in order to get the best results, also the use of an implicit solvation model goes a long way. The output displays the value of the total isotropic magnetic shielding for each nucleus in ppm (image taken from the Gaussian website):

Magnetic shielding (ppm): 1 C Isotropic = 57.7345 Anisotropy = 194.4092 XX= 48.4143 YX= .0000 ZX= .0000 XY= .0000 YY= -62.5514 ZY= .0000 XZ= .0000 YZ= .0000 ZZ= 187.3406 2 H Isotropic = 23.9397 Anisotropy = 5.2745 XX= 27.3287 YX= .0000 ZX= .0000 XY= .0000 YY= 24.0670 ZY= .0000 XZ= .0000 YZ= .0000 ZZ= 20.4233

Now, here is why this is the long way; in order for these values to be meaningful they need to be contrasted with a reference, which experimentally for ^{1}H and ^{13}C is tetramethylsilane, TMS. This means you have to perform the same calculation for TMS at -preferably- the same level of theory used for the sample and substract the corresponding values for either H or C accordingly. Only then the chemical shifts will read as something we can all remember from basic analytical chemistry class.

GaussView 6.0 provides a shortcut; open the Results menu, select NMR and in the new window there is a dropdown menu for selecting the nucleus and a second menu for selecting a reference. In the case of hydrogen the available references are TMS calculated with the HF and B3LYP methods. The SCF – GIAO plot will show the assignments to each atom, the integration simulation and a reference curve if desired.

The chemical shifts obtained this far will be a good approximation and will allow you to assign any peaks in any given spectrum but still not be completely accurate though. The reasons behind the numerical deviations from calculated and experimental values are many, from the chosen method to solvent interactions or basis set limitations, scaling factors are needed; that’s when you can ask the Cheshire Cat which way to go

If you don’t know where you are going any road will get you there.

Lewis Carroll – Alice in Wonderland

Well, not really. The Chemical Shift Repository for computed NMR scaling factors, with Coupling Constants Added Too (aka CHESHIRE CCAT) provides with straight directions on how to correct your computed NMR chemical shifts according to the level of theory without the need to calculate the NMR shielding tensor for the reference compound (usually TMS as pointed out earlier). In a nutshell, the group of Prof. Dean Tantillo (UC Davis) has collected a large number of isotropic magnetic shielding values and plotted them against experimental chemical shifts. Just go to their scaling factors page and check all their linear regressions and use the values that more closely approach to your needs, there are also all kinds of scripts and spreadsheets to make your job even easier. Of course, if you make use of their website **don’t forget** to give the proper credit by including these references in your paper.

We’ve recently published an interesting study in which the 1H – 19F coupling constants were calculated via the long way (I was just recently made aware of CHESHIRE CCAT by Dr. Jacinto Sandoval who knows all kinds of web resources for computational chemistry calculations) as well as their conformational dependence for some substituted 2-aza-carbazoles (fig. 1).

The paper is published in the Journal of Molecular Structure. In this study we used the GIAO NMR computations to assign the peaks on an otherwise cluttered spectrum in which the signals were overlapping due to conformational variations arising from the rotation of the C-C bond which re-orients the F atoms in the fluorophenyl grou from the H atom in the carbazole. After the calculations and the scans were made assigning the peaks became a straightforward task even without the use of scaling factors. We are now expanding these calculations to more complex systems and will contrast both methods in this space. Stay tuned.

## Post Calculation Addition of Empirical Dispersion – Fixing interaction energies

Calculation of interaction energies is one of those things people are more concerned with and is also something mostly done wrong. The so called ‘*gold standard*‘ according to Pavel Hobza for calculating supramolecular interaction energies is the CCSD(T)/CBS level of theory, which is highly impractical for most cases beyond 50 or so light atoms. Basis set extrapolation methods and inclusion of electronic correlation with MP2 methods yield excellent results but they are not nonetheless almost as time consuming as CC. DFT methods in general are terrible and still are the most widely used tools for electronic structure calculations due to their competitive computing times and the wide availability of schemes for including terms which help describe various kinds of interactions. The most important ingredients needed to get a decent to good interaction energies values calculated with DFT methods are correlation and dispersion. The first part can be recreated by a good correlation functional and the use of empirical dispersion takes care of the latter shortcoming, dramatically improving the results for interaction energies even for lousy functionals such as the infamous B3LYP. The results still wont be of benchmark quality but still the deviations from the *gold standard* will be shortened significantly, thus becoming more quantitatively reliable.

There is an online tool for calculating and adding the empirical dispersion from Grimme’s group to a calculation which originally lacked it. In the link below you can upload your calculation, select the basis set and functionals employed originally in it, the desired damping model and you get in return the corrected energy through a geometrical-Counterpoise correction and Grimme’s empirical dispersion function, D3, of which I have previously written here.

The gCP-D3 Webservice is located at: http://wwwtc.thch.uni-bonn.de/

The platform is entirely straightforward to use and it works with xyz, turbomole, orca and gaussian output files. The concept is very simple, a both gCP and D3 contributions are computed in the selected basis set and added to the uncorrected DFT (or HF) energy (eq. 1)

(**1**)

If you’re trying to calculate interaction energies, remember to perform these corrections for every component in your supramolecular assembly (eq. 2)

(**2**)

Here’s a screen capture of the outcome after uploading a G09 log file for the simplest of options B3LYP/6-31G(*d*), a decomposed energy is shown at the left while a 3D interactive Jmol rendering of your molecule is shown at the right. Also, various links to the literature explaining the details of these calculations are available in the top menu.

I’m currently writing a book chapter on methods for calculating ineraction energies so expect many more posts like this. A special mention to Dr. Jacinto Sandoval, who is working with us as a postdoc researcher, for bringing this platform to my attention, I was apparently living under a rock.

## Error for Gaussian16 .log files and GaussView5

There’s an error message when opening some Gaussian16 output files in GaussView5 for which the message displayed is the following:

ConnectionGLOG::Parse_Gauss_Coord(). Failure reading oriented atomic coordinates. Line Number

We have shared some solutions to the GaussView handling of *chk and *.fchk files in teh past but never for *.log files, and this time Dr. Davor Šakić from the University of Zagreb in Croatia has brought to my attention a fix for this error. If “Dipole orientation” with subsequent orientation is removed, the file becomes again readable by GaussView5.

Here you can download a script to fix the file without any hassle. The usage from the command line is simply:

˜$ chmod 777 Fg16TOgv5 ˜$ ./Fg16TOgv5 name.log

The first line is to change and grant all permissions to the script (use at your discretion/own risk), which in turn will take the output file **name.log** and yield two more files: **gv5_name.log** and and **name.arch**; the latter archive allows for easy generation of SI files while the former is formatted for GaussView5.x.

Thanks to Dr. Šakić for his script and insight, we hope you find it useful and if indeed you do please credit him whenever its due, also, if you find this or other posts in the blog useful, please let us know by sharing, staring and commenting in all of them, your feedback is incredibly helpful in justifying to my bosses the time I spent curating this blog.

Thanks for reading.

## fchk file errors (Gaussian) Missing or bad Data: RBond

We’ve covered some common errors when dealing with formatted checkpoint files (*.fchk) generated from Gaussian, specially when analyzed with the associated GaussView program. (see here and here for previous posts on the matter.)

Prof. Neal Zondlo from the University of Delaware kindly shared this solution with us when the following message shows up:

CConnectionGFCHK::Parse_GFCHK() Missing or bad data: Rbond Line Number 1234

The Rbond label has to do with the connectivity displayed by the visualizer and can be overridden by close examination of the input file. In the example provided by Prof. Zondlo he found the following line in the connectivity matrix of the input file:

2 9 0.0

which indicates a zero bond order between atoms 2 and 9, possibly due to their proximity. He changed the line to simply

2

So editing the connectivity of your atoms in the input can help preventing the Rbond message.

I hope this helps someone else.

## The “art” of finding Transition States Part 2

Last week we posted some insights on finding Transitions States in Gaussian 09 in order to evaluate a given reaction mechanism. A stepwise methodology is tried to achieve and this time we’ll wrap the post with two flow charts trying to synthesize the information given. It must be stressed that knowledge about the chemistry of the reaction is of paramount importance since G09 cannot guess the structure connecting two minima on its own but rather needs our help from our chemical intuition. So, without further ado here is the remainder of Guillermo’s post.

**METHOD 3. **QST3. For this method, you provide the coordinates of your reagents, products and TS (in that order) and G09 uses the QST3 method to find the first order saddle point. As for QST2 the numbering scheme must match for all the atoms in your three sets of coordinates, again, use the connection editor to verify it. Here is an example of the input file.

link 0 --blank line-- #p b3lyp/6-31G(d,p)opt=(qst3,calcfc)geom=connectivity freq=noraman --blank line--Charge MultiplicityCoordinates of reagents --blank line—Charge MultiplicityCoordinates of products --blank line--Charge MultiplicityCoordinates of TS --blank line---

As I previously mentioned, it happens that you find a first order saddle point but does not correspond to the TS you want, you find an imaginary vibration that is not the one for the bond you are forming or breaking. For these cases, I suggest you to take that TS structure and manually modify the region that is causing you trouble, then use method 2.

**METHOD 4. **When the previous methods fail to yield your desired TS, the brute force way is to acquire the potential energy surface (PES) and visually locate your possible TS. The task is to perform a rigid PES scan, for this, the molecular structure must be defined using z-matrix. Here is an example of the input file.

link 0 --blank line-- #p b3lyp/6-31G(d,p)scan testgeom=connectivity --blank line--Charge MultiplicityZ-matrix of reagents (or products) --blank line--

In the Z-matrix section you must specify which variables (B, A or D) you want to modify. First, locate the variables you want to modify (distance B, angle A, or dihedral angle D). Then modify those lines within the Z-matrix, here is an example.

B1 1.41 3 0.05 A1 104.5 2 1.0

What you are specifying with this is that the variable B1 (a distance) is going to be stepped 3 times by 0.05. Then variable A1 (an angle) is going to be stepped 2 times by 1.0. Thus, a total of 12 energy evaluations will be performed. At the end of the calculation open the .log file in gaussview and in Results choose the Scan… option. This will open a 3D surface where you should locate the saddle point, this is an educated guess, so take the structure you think corresponds to your TS and use it for method 2.

I have not fully explored this method so I encourage you to go to Gaussian.com and thoroughly review it.

Once you have found your TS structure and via the imaginary vibration confirmed that is the one you are looking for the next step is to verify that your TS connects both your reagents and products in the potential energy surface. For this, an Intrinsic Reaction Coordinate (IRC) calculation must be performed. Here is an example of the input file for the IRC.

link 0 --blank line-- #p b3lyp/6-31G(d,p)irc=calcfcgeom=connectivity --blank line--Charge MultiplicityCoordinates of TS --blank line--

With this input, you ask for an IRC calculation, the default numbers of steps are 20 for each side of your TS in the PES; you must specify the coordinates of your TS or take them from the .chk file of your optimization. In addition, an initial force constant calculation must be made. It often occurs that the calculation fails in the correction step, thus, for complicated cases I hardly suggest to use **irc=calcall**, this will consume very long time (even days) but there is a 95% guaranty. If the number of points is insufficient you can put more within the route section, here is such an example for a complicated case.

link 0 --blank line-- #p b3lyp/6-31G(d,p)irc=(calcall,maxpoints=80)geom=connectivity --blank line--Charge MultiplicityCoordinates of TS --blank line--

With this route section, you are asking to perform an IRC calculation with 80 points on each side of the PES, calculating the force constants at every point. For an even complicated case try adding the **scf=qc** keyword in the route section, quadratic convergence often works better for IRC calculations.