Category Archives: Gaussian

Geometry Optimizations for Excited States


Electronic excitations are calculated vertically according to the Frank—Condon principle, this means that the geometry does not change upon the excitation and we merely calculate the energy required to reach the next electronic state. But for some instances, say calculating not only the absorption spectra but also the emission, it is important to know what the geometry minimum of this final state looks like, or if it even exists at all (Figure 1). Optimizing the geometry of a given excited state requires the prior calculation of the vertical excitations whether via a multireference method, quantum Monte Carlo, or the Time Dependent Density Functional Theory, TD-DFT, which due to its lower computational cost is the most widespread method.

Most single-reference treatments, ab initio or density based, yield good agreement with experiments for lower states, but not so much for the higher excitations or process that involve the excitation of two electrons. Of course, an appropriate selection of the method ensures the accuracy of the obtained results, and the more states are considered, the better their description although it becomes more computationally demanding in turn.

Figure 1. The vertical excitation does not match the minimum on the excited state

In Gaussian 09 and 16, the argument to the ROOT keyword selects a given excited state to be optimized. In the following example, five excited states are calculated and the optimization is requested upon the second excited state. If no ROOT is specified, then the optimization would be carried out by default on the first excited state (Where L.O.T. stands for Level of Theory).

#p opt TD=(nstates=5,root=2) L.O.T.

Gaussian16 includes now the calculation of analytic second derivatives which allows for the calculation of vibrational frequencies for IR and Raman spectra, as well as transition state optimization and IRC calculations in excited states opening thus an entire avenue for the computation of photochemistry.

If you already computed the excited states and just want to optimize one of them from a previous calculation, you can read the previous results with the following input :

#p opt TD=(Read,Root=N) L.O.T. Density=Current Guess=Read Geom=AllCheck

Common problems. The following error message is commonly observed in excited state calculations whether in TD-DFT, CIS or other methods:

No map to state XX, you need to solve for more vectors in order to follow this state.

This message usually means you need to increase the number of excited states to be calculated for a proper description of the one you’re interested in. Increase the number N for nstates=N in the route section at higher computational cost. A rule of thumb is to request at least 2 more states than the state of interest. This message can also reflect the fact that during the optimization the energy ordering changes between states, and can also mean that the ground state wave function is unstable, i.e., the energy of the excited state becomes lower than that of the ground state, in this case a single determinant approach is unviable and CAS should be used if the size of the molecule allows it. Excited state optimizations are tricky this way, in some cases the optimization may cross from one PES to another making it hard to know if the resulting geometry corresponds to the state of interest or another. Gaussian recommends changing the step size of the optimization from the default 0.3 Bohr radius to 0.1, but obviously this will make the calculation take longer.

Opt=(MaxStep=10)

If the minimum on the excited state potential energy surface (PES) doesn’t exist, then the excited state is not bound; take for example the first excited state of the H2 molecule which doesn’t show a minimum, and therefore the optimized geometry would correspond to both H atoms moving away from each other indefinitely (Figure 2). Nevertheless, a failed optimization doesn’t necessarily means the minimum does not exist and further analysis is required, for instance, checking the gradient is converging to zero while the forces do not.

Figure 2. An unbound excited state with no minima ensures the dissociation of the system along the reaction coordinate

Basis Set Superposition Error (BSSE). A short intro


Molecular Orbitals (MOs) are linear combinations of Atomic Orbitals (AOs), which in turn are linear combinations of other functions called ‘basis functions’. A basis, or more accurately a basis set, is a collection of functions which obey a set of rules (such as being orthogonal to each other and possibly being normalized) with which all AOs are constructed, and although these are centered on each atomic nucleus, the canonical way in which they are combined yield delocalized MOs; in other words, an MO can occupy a large space spanning several atoms at once. We don’t mind this expansion across a molecule, but what about between two molecules? Calculating the interaction energy between two or more molecular fragments leads to an artificial extra–stabilization term that stems from the fact that electrons in molecule 1 can occupy AO’s (or the basis functions which form them) centered on atoms from molecule 2.

Fundamentally, the interaction energy of any A—B dimer, Eint, is calculated as the energy difference between the dimer and the separately calculated energies for each component (Equation 1).

Eint = EAB – EA – EB (1)

However the calculation of Eint by this method is highly sensitive to the choice of basis set due to the Basis Set Superposition Error (BSSE) described in the first paragraph. The BSSE is particularly troublesome when small basis sets are used, due to the poor description of dispersion interactions but treating this error by just choosing a larger basis set is seldom useful for systems of considerable sizes. The Counterpoise method is a nifty correction to equation 1, in which EA and EB are calculated with the basis set of A and B respectively, i.e., only in EAB a larger basis set (that of A and B simultaneously) is used. The Counterpoise method calculates each component with the AB basis set (Equation 2)

EintCP = EABAB – EAAB– EBAB (2)

where the superscript AB means the whole basis set is used. This is accomplished by using ‘ghost‘ atoms with no nuclei and no electrons but empty basis set functions centered on them.

In Gaussian, BSSE is calculated with the Counterpoise method developed by Boys and Simon. It requires the keyword Counterpoise=N where N is the number of fragments to be considered (for an A—B system, N=2). Each atom in the coordinates list must be specified to which fragment pertains; additionally, the charge and multiplicity for each fragment and the whole supermolecular ensemble must be specified. Follow the example of this hydrogen fluoride dimer.

%chk=HF2.chk
#P opt wB97XD/6-31G(d,p) Counterpoise=2

HF dimer

0,1 0,1 0,1
H(Fragment=1) 0.00 0.00 0.00
F(Fragment=1) 0.00 0.00 0.70
H(Fragment=2) 0.00 0.00 1.00
F(Fragment=2) 0.00 0.00 1.70

For closed shell fragments the first line is straightforward but one must pay attention that the first pair of numbers in the charge multiplicity line correspond to the whole ensemble, whereas the folowing pairs correspond to each fragment in consecutive order. Fragments do not need to be specified contiguously, i.e., you don’t need to define all atoms for fragment 1 and after those the atoms for fragment 2, etc. They could be mixed and the program still assigns them correctly. Just as an example I typed wB97XD but any other method, DFT or ab initio, may be used; only semiempirical methods do not admit a BSSE calculation because they don’t make use of a basis set in the first place!

The output provides the corrected energy (in atomic units) for the whole system, as well as the BSSE correction (which added to the previous term yields the un-corrected energy of the system). Gaussian16 also provides these values in kcal/mol as ‘Complexation energies’ first raw (uncorrected) and then the corrected energy.

BSSE is always present and cannot be entirely eliminated because of the use of finite basis sets but it can be correctly dealt with if the Counterpoise method is included.

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) LOT Density=Current Guess=Read Geom=AllCheck

replace N for the Nth 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 Nth 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.

Natural Transition Orbitals (NTOs) Gaussian


The canonical molecular orbital depiction of an electronic transition is often a messy business in terms of a ‘chemical‘ interpretation of ‘which electrons‘ go from ‘which occupied orbitals‘ to ‘which virtual orbitals‘.

Natural Transition Orbitals provide a more intuitive picture of the orbitals, whether mixed or not, involved in any hole-particle excitation. This transformation is particularly useful when working with the excited states of molecules with extensively delocalized chromophores or multiple chromophoric sites. The elegance of the NTO method relies on its simplicity: separate unitary transformations are performed on the occupied and on the virtual set of orbitals in order to get a localized picture of the transition density matrix.

[1] R. L. Martin, J. Chem. Phys., 2003, DOI:10.1063/1.1558471.

In Gaussian09:
After running a TD-DFT calculation with the keyword TD(Nstates=n) (where n = number of states to be requested) we need to take that result and launch a new calculation for the NTOs but lets take it one step at a time. As an example here’s phenylalanine which was already optimized to a minimum at the B3LYP/6-31G(d,p) level of theory. If we take that geometry and launch a new calculation with the TD(Nstates=40) in the route section we obtain the UV-Vis spectra and the output looks like this (only the first three states are shown):

Excitation energies and oscillator strengths:

Excited State 1: Singlet-A 5.3875 eV 230.13 nm f=0.0015 <S**2>=0.000
42 -> 46 0.17123
42 -> 47 0.12277
43 -> 46 -0.40383
44 -> 45 0.50838
44 -> 47 0.11008
This state for optimization and/or second-order correction.
Total Energy, E(TD-HF/TD-KS) = -554.614073682
Copying the excited state density for this state as the 1-particle RhoCI density.

Excited State 2: Singlet-A 5.5137 eV 224.86 nm f=0.0138 <S**2>=0.000
41 -> 45 -0.20800
41 -> 47 0.24015
42 -> 45 0.32656
42 -> 46 0.10906
42 -> 47 -0.24401
43 -> 45 0.20598
43 -> 47 -0.14839
44 -> 45 -0.15344
44 -> 47 0.34182

Excited State 3: Singlet-A 5.9254 eV 209.24 nm f=0.0042 <S**2>=0.000
41 -> 45 0.11844
41 -> 47 -0.12539
42 -> 45 -0.10401
42 -> 47 0.16068
43 -> 45 -0.27532
43 -> 46 -0.11640
43 -> 47 0.16780
44 -> 45 -0.18555
44 -> 46 -0.29184
44 -> 47 0.43124

The oscillator strength is listed on each Excited State as “f” and it is a measure of the probability of that excitation to occur. If we look at the third one for this phenylalanine we see f=0.0042, a very low probability, but aside from that the following list shows what orbital transitions compose that excitation and with what energy, so the first line indicates a transition from orbital 41 (HOMO-3) to orbital 45 (LUMO); there are 10 such transitions composing that excitation, visualizing them all with canonical orbitals is not an intuitive picture, so lets try the NTO approach, we’re going to take excitation #10 for phenylalanine as an example just because it has a higher oscillation strength:

%chk=Excited State 10: Singlet-A 7.1048 eV 174.51 nm f=0.3651 <S**2>=0.000
41 -> 45 0.35347
41 -> 47 0.34685
42 -> 45 0.10215
42 -> 46 0.17248
42 -> 47 0.13523
43 -> 45 -0.26596
43 -> 47 -0.22995
44 -> 46 0.23277

Each set of NTOs for each transition must be calculated separately. First, copy you filename.chk file from the TD-DFT result to a new one and name it after the Nth state of interest as shown below (state 10 in this case). NOTE: In the route section, replace N with the number of the excitation of interest according to the results in filename.log. Run separately for each transition your interested in:

#chk=state10.chk

#p B3LYP/6-31G(d,p) Geom=AllCheck Guess=(Read,Only) Density=(Check,Transition=N) Pop=(Minimal,NTO,SaveNTO)

0 1
--blank line--

By requesting SaveNTO, the canonical orbitals in the state10.chk file are replaced with the NTOs for the 10th excitation, this makes it easier to plot since most visualizers just plot whatever set of orbitals they read in the chk file but if they find the canonical MOs then one would need to do some re-processing of them. This is much more straightforward.

Now we format our chk files into fchk with the formchk utility:

formchk -3 filename.chk filename.fchk
formchk -3 state10.chk state10.fchk

If we open filename.fchk (the file where the original TD-DFT calculation is located) with GaussView we can plot all orbitals involved in excited state number ten, those would be seven orbitals from 41 (HOMO-3) to 47 (LUMO+2) as shown in figure 1.

Figure 1. Canonical orbitals involved in the 10th excited state according to the TD-DFT calculation

If we now open state10.fchk we see that the numbers at the side of the orbitals are not their energy but their occupation number particular to this state of interest, so we only need to plot those with highest occupations, in our example those are orbitals 44 and 45 (HOMO and LUMO) which have occupations = 0.81186; you may include 43 and 46 (HOMO-1 and LUMO+1, respectively) for a much more complete description (occupations = 0.18223) but we’re still dealing with 4 orbitals instead of 7.

Figure 2. Natural Transition Orbitals for Phenylalanine. Orbital 44 (particle) and Orbital 45 (hole) exhibit the largest occupations for Excited State No. 10

The NTO transition 44 -> 45 is far easier to conceptualize than all the 10 combinations given in the canonical basis from the direct TD-DFT calculation. TD-DFT provides us with the correct transitions, NTOs just paint us a picture more readily available to the chemist mindset.

NOTE: for G09 revC and above, the %OldChk option is available, I haven’t personally tried it but using it to specify where the excitations are located and then write the NTOs of interest into a new chk file in the following way, thus eliminating the need of copying the original chk file for each state:

%OldChk=filename.chk
%chk=stateN.chk

NTOs are based on the Natural Hybrid orbitals vision by Löwdin and others, and it is said to be so straightforward that it has been re-discovered from time to time. Be that as it may, the NTO visualization provides a much clearer vision of the excitations occurring during a TD calculation.

Thanks for reading, stay home and stay safe during these harsh days everyone. Please share, rate and comment this and other posts.

Useful Thermochemistry from Gaussian Calculations


Statistical Mechanics is the bridge between microscopic calculations and thermodynamics of a particle ensemble. By means of calculating a partition function divided in electronic, rotational, translational and vibrational functions, one can calculate all thermodynamic functions required to fully characterize a chemical reaction. From these functions, the vibrational contribution, together with the electronic contribution, is the key element to getting thermodynamic functions.

Calculating the Free Energy change of any given reaction is a useful approach to asses their thermodynamic feasibility. A large negative change in Free Energy when going from reagents to products makes up for a quantitative spontaneous (and exothermic) reaction, nevertheless the rate of the reaction is a different story, one that can be calculated as well.

Using the freq option in your route section for a Gaussian calculation is mandatory to ascertain the current wave function corresponds to a minimum on a potential energy hypersurface, but also yields the thermochemistry and thermodynamic values for the current structure. However, thermochemistry calculations are not restricted to minima but it can also be applied to transition states, therefore yielding a full thermodynamic characterization of a reaction mechanism.

A regular freq calculation yields the following output (all values in atomic units):

Zero-point correction=                           0.176113 (Hartree/Particle)
 Thermal correction to Energy=                    0.193290
 Thermal correction to Enthalpy=                  0.194235
 Thermal correction to Gibbs Free Energy=         0.125894
 Sum of electronic and zero-point Energies=           -750.901777
 Sum of electronic and thermal Energies=              -750.884600
 Sum of electronic and thermal Enthalpies=            -750.883656
 Sum of electronic and thermal Free Energies=         -750.951996

For any given reaction say A+B -> C one could take the values from the last row (lets call it G) for all three components of the reaction and perform the arithmetic: DG = GC – [GA + GB], so products minus reagents.

By default, Gaussian calculates these values (from the previously mentioned partition function) using normal conditions, T = 298.15 K and P = 1 atm. For an assessment of the thermochemistry at other conditions you can include in your route section the corresponding keywords Temperature=x.x and Pressure=x.x, in Kelvin and atmospheres, respectively.

(Huge) Disclaimer: Although calculating the thermochemistry of any reaction by means of DFT calculations is a good (and potentially very useful) guide to chemical reactivity, getting quantitative results require of high accuracy methods like G3 or G4 methods, collectively known as Gn mehtods, which are composed of pre-defined stepwise calculations. The sequence of these calculations is carried out automatically; no basis set should be specified. Other high accuracy methods like CBS-QB3 or W1U can also be considered whenever Gn methods are too costly.

Atom specifications unexpectedly found in input stream.


“Well, where else were they supposed to appear?”

I was sent this error along with the previous question for a failed optimization. Apparently there is no answer in the internet (I quickly checked) so here it is:

Gaussian is confused about finding atomic coordinates because there is also a geom=check instruction placed in the route section, i.e., it was told to retrieve the atomic coordinates from a checkpoint and then it was given those atomic coordinates within the input so it doesn’t know what you mean and exits.

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 1H and 13C 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 1H and 13C  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).

1-s2.0-S0022286018310330-fx1_lrg

Journal of Molecular Structure Vol 1176, 15 January 2019, Pages 562-566

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.

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.

Python scripts for calculating Fukui Indexes


One of the most popular posts in this blog has to do with calculating Fukui indexes, however, when dealing with a large number of molecules, our described methodology can become cumbersome since it requires to manually extract the population analysis from two or three different output files and then performing the arithmetic on them separately with a spreadsheet or something.

Our new team member Ricardo Loaiza has written a python script that takes the three aforementioned files and yields a .csv file with the calculated Fukui indexes, and it even points out which of the atoms exhibit the largest values so if you have a large molecule you don’t have to manually check for them. We have also a batch version which takes all the files in any given directory and performs the Fukui calculations for each, provided it can find file triads with the naming requirements described below.

Output files must be named filename.log (the N electrons reference state), filename_plus.log (the state with N+1 electrons) and filename_minus.log (the N-1 electrons state). Another restriction is that so far these scripts only work with NBO population analysis as provided by the NBO3.1 program available in the various versions of Gaussian. I imagine the listing is similar in NBO5.x and NBO6.x and so it should work if you do the population analysis with them.

The syntax for the single molecule version is:

python fukui.py filename.log filename_minus.log filename_plus.log

For the batch version is:

./fukuiPorLote.sh

(Por Lote means In Batch in Spanish.)

These scripts are available via GitHub. We hope you find them useful, and you do please let us know whether here at the comments section or at our GitHub site.

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.

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