The aim of
this blog is to promote the development of computation chemistry, at least to a
small extent.

Besides
that, let me introduce my programs:

The aim of
this blog is to promote the development of computation chemistry, at least to a
small extent.

Besides
that, let me introduce my programs:

Sometimes users ask us to implement a feature
like plotting multiple spectra (from different files) in a single graph. We do
not plan to implement such features, because:

1) This
will require a reconstruction of the user interface, and old users will have to
learn how to use Chemcraft again;

2) For building graphs of any type, powerful
software packages already exist – Excel, Origin, etc. We do not want to compete
with them. But Chemcraft allows one to export any graph, spectrum, diagram in
text format, copying its data to Excel via Clipboard. So, multiple spectra in
one picture can be easily obtained as follows: you should open several output
files in a row, copy the data with spectra to Excel and then combine these
spectra in Excel. Note that the broadened spectrum (Doppler, Lorentzian
broadening of bands) can be exported too.

See, for example, this graph built in
Chemcraft:

This is a Gaussian09 Born-Oppenheimer
Molecular Dynamics (BOMD) computation, and the graph shows the distance between
atoms C1 and H1 versus time in femtoseconds. There seems to be a problem, or a bug,
with visualization of such files – Chemcraft reads the first 3 points with zero
time. We found the format of the output file quite difficult. Maybe this
problem will be fixed in future, but we are not even sure that this is
necessary: if you need to plot a good graph “Distance vs Time”, click on the
“Copy” button, insert the data into Excel and manually delete the invalid
lines. Of course you should check your graph against the output file – if you
work with BOMD computations, you should understand them well enough.

We always give our users the possibility to
verify the data visualization in Chemcraft – for example, when you visualize
the molecular orbitals, you can click the “Check orbitals” button to check
whether Chemcraft extracted all orbitals correctly. When we implement
visualization of MOS from output files of new software, it is sometimes
difficult to thoroughly verify whether the MOS are visualized correctly
(probably free software is characterized with such problems to a greater
extent). And don’t forget to check the data shown by Chemcraft using the Source
mode.

We have
gathered some information from computational chemistry forums, which can be
helpful for you. It should be noted that the following text cannot be
considered as a professional guide; such guides will possibly appear in the
future.

First of
all, you should read this manual:

One of the thesises in this book is that the GGA functionals are ususally more universal (let’s say, closer to
“Ab initio”) than the hybrid functionals (this statement, however, has some weak points). This also means that the errors with
these functionals are more systematic: for example, the PBE functional usually
overestimates the bond lengths and underestimates the vibrational frequencies.
In our opinion, if you choose between, e.g., the PBE and B3LYP functionals, you
should note that the latter should be more accurate for most organic molecules,
but it should be less accurate in some problematic cases; so, the PBE
functional is more reliable. Because of that, at one forum we found the
following advice (written in 2010): always use the PBE functional and don’t
worry. It is CGA, so it must be more universal than, e.g., the B3LYP functional.

It is written in this manual that the B3LYP
functional has shown good results for organic molecules, but it is worse for
transition metal compounds and for large molecules. TPSSh probably is a good functional for transition metal compounds (according to this manual).

The B3LYP functional is commonly used in chemistry, while the PBE, PBE0 functionals are commonly used in applications to extended systems (materials) [13].

Here is
another compilation on the subject:

Here is a
screenshot from this paper:

It is not
clear from this list, whether the dispersion correction should be always used.
However, at other forums we found the advices to use the dispersion correction
always if possible. In Ref. [1] you can see that the ωB97X-D is the best single-component
functional, while PBE0-D3 perform almost as well. Besides that, on the CCL list one can read that B3LYP-D3 is usually better than B3LYP.

Dispersion
correction is the interaction of induced dipoles. This correction becomes
important if two parallel benzene rings interact (stacking). So, the dispersion
correction is important for computing such molecules as tetraphenylporphyrin, bilirubin,
etc.

Here is a
list of favorable and non-favorable DFT functionals from the DFT 2015 poll for
computing particular properties:

With all due respect to the creators of the
above list, we must mention that we tried to compute the properties of
bilirubin molecule (having intermolecular H-bonds) using the PBE, B3LYP and wB97XD
functionals, and we found that the PBE functional is the worst at describing intermolecular
H bonds (the PMR spectra computed using the PBE/6-311G(D,P) method are in
poorer agreement with the experimental ones than the PMR spectra computed using
the B3LYP/6-311G(D,P) or wB97XD/6-311G(D,P) methods). So, we found that the PBE
functional is not good at describing H-bonds, in contrast to the conclusions
drawn above. So, we think that you should not fully trust these tables.

Another
post from CCL states the following:

- Recommended GGA methods: revPBE-D3, B97-D3

- Recommended meta-GGA methods: oTPSS-D3,
TPSS-D3

- Hybrid functionals: PW6B95-D3, M062X-D3

- Double-hybrids are the most accurate DFT
methods on the market: DSD-BLYP-D3, DSD-PBEP86-D3, PWPB95-D3

In Ref. [2], a thorough energy benchmark
study of various density functionals (DFs) was carried out. The authors write:

“In
summary, we recommend on the GGA level the B97-D3 and revPBE-D3 functionals.
The best meta-GGA is oTPSS-D3 although meta-GGAs represent in general no clear
improvement compared to numerically simpler GGAs. Notably, the widely used
B3LYP functional performs worse than the average of all tested hybrids and is
also very sensitive to the application of dispersion corrections.”

“The
ωB97X-D functional seems to be a promising method. The most robust hybrid is
Zhao and Truhlar's PW6B95 functional in combination with DFT-D3”.

“If higher
accuracy is required, double-hybrids should be applied. The corresponding
DSD-BLYP-D3 and PWPB95-D3 variants are the most accurate and robust functionals
of the entire study.”

The tests
in this paper were performed on GMTKN30 set – this set covers mainly molecules
containing main group elements, mostly organic (link).

So, the double-hybrids seem to be the best
DFT methods at the moment. This is illustrated by the following chart from the
aforementioned paper:

Another
advantage of PBE is that this functional is “cheap”.

Note that
the PBE and PBE0 methods are quite different: PBE is a CGA, while PBE0 is a hybrid method. However, if one compares e.g. BP86, BLYP, BPW91 functionals (GGA) with PBE0, he finds that PBE0 is "less semi-empirical".

Here is
another comparison of DFT functionals. In Ref. [3], a few DFT functionals were benchmarked
for 14 compounds (calculation of vertical excitation energies by TDDFT and their
comparison to experiment). Here are two pictures from this
paper:

Ref. [4]
reports that the CAM-B3LYP and BHandH functionals yield the best agreement
between computed and experimental vertical absorption energies for a set of
some simple organic molecules (involving first and second row atoms).

The
combination of these advices can confuse an inexperienced user. As for us, we
decided that we should use PBE-D3 for inorganic molecules and ωB97X-D or
B3LYP-D3 for organic ones, since we deal with the Gaussian09A package. Such an
advice should be useful only for “amateurs” who are unable to gather more
information.

Anyway, it is better to use several
functionals to ensure that they produce similar results. MP2 should
not also be forgotten (SCS-MP2 seems to be better than conventional MP2, as written in the paper
above; as far as we know, SOS-MP2 is better too).

Recently, the B3LYP/6-31G(D,P) method has
been quite popular. We think that using this method for computing organic
molecules (not containing d and f elements) is still rather adequate, but the
snobs can interpret the use of this method as the sign of amateurishness (at
least, if you don’t employ different functionals and/or basis sets in the same
study). See, for example, this and this posts on the CCL list.

The flaws of this famous B3LYP/6-31G* model
chemistry are discussed in Ref. [5]:

The authors write that the relatively good
performance of B3LYP/6-31G*, which made it so popular, is caused by a hidden
error cancellation. The B3LYP-gCP-D3/6-31G* method, according to the authors, is
much better (it removes the two major deficiencies: missing London dispersion effects and basis set
superposition error). The B3LYP-D3/6-31G* method is slightly worse as it does
not provide a BSSE elimination. This picture illustrates the aforesaid:

As far as
we know, the density fitting / RI (Resolution of the Identity) approximation is usually a good thing,
as it speeds up your calculations without significant loss of accuracy (it least, this is written in Orca manual). However, in
some cases it can lead to bad SCF convergence or give the error of 1-2 kcal/mol
in energies.

Here is a picture from Ref. [13] illustrating the availability of DFT functionals:

As far as we know, at the moment the optimal basis sets for high-accuracy computations are Dunning family sets: cc-pVnZ, aug-cc-pVnZ, cc-pCVnZ, cc-pwCVnZ (n=2,3.4,5,
etc). These basis sets are correlation consistent; this means, that they were
optimized using correlated methods, unlike the 6-31G** basis sets. In Ref. [6] the following is stated:

"One of the primary reasons for the cc basis set family’s lasting

popularity is due to a series of empirical observations that as

the cardinal number (n in cc-pVnZ) of the basis set is increased,

energies and various properties converge smoothly toward the

complete basis set (CBS) limit."

"One of the primary reasons for the cc basis set family’s lasting

popularity is due to a series of empirical observations that as

the cardinal number (n in cc-pVnZ) of the basis set is increased,

energies and various properties converge smoothly toward the

complete basis set (CBS) limit."

The so-called complete basis set (CBS) limit means that you first compute with cc-pVDZ, then cc-pVTZ,
then cc-pVQZ, then cc-pV5Z, etc., and the energy should converge to a
hypothetical “complete” basis set limit. At the same time, there are more than 10 extrapolation schemes which give nearly the same result after performing only 2-3 computations (however, these extrapolation schemes are empirical to some extent).

For heavy elements (Z>29), relativistic effects are
strong and must be taken into account either using the methods like ZORA, DKH, or
using effective core potentials (ECPs, PPs). The main relativistic effects include relativistic contraction and spin-orbit interaction. For many tasks, even such elements as Fe, Co, Ni do not require including relativistic effects in the computation (you will have a lot of problems besides relativism with these atoms).

The Ref. [6] provides an overview of the
development of Gaussian basis sets for molecular calculations, with a focus on
four popular families of modern bases ("Gaussian basis set" means any basis set with Gaussian (not Slater) functions, not a specific set for the GAUSSIAN program). The authors write about the cases when
using ECPs is not advisable (in particular, electron paramagnetic resonance),
and it is written that using the DFT-based ZORA or DKH models with segmented
all-electron relativistic contracted (SARC) basis sets produce good agreement
with experiment and higher level ab initio computations.

One interesting point is mentioned in Ref.
[7]: the authors report that the computations with 6-311++G** basis set gave
better molecular geometries than the more costly aug-cc-pVDZ (the methods used
were MP2 and CCSD). In addition, the smaller 6-311++G** invariably leads to
lower calculated total energies than aug-cc-pVDZ. So, it seems that the aug-cc-pVDZ
can be worse than the 6-311++G** set (nevertheless, we suppose that if you need an
expensive basis set or CBS (complete basis set) extrapolation, you should use cc-pVTZ,
cc-pVQZ, cc-pV5Z, etc).

Some people
say that it is not actual to use basis sets larger than cc-pVTZ with DFT. However,
in Ref. [14] the authors performed energy computations of 211 small first and
second row compounds (mostly organic), and they concluded that the 5Z basis set
(aug-cc-pV5Z) is required to get the MAE of atomization energies below 1
kcal/mol. See this blog for more information.

The same is
written at this handbook “Practical Advice for Quantum Chemistry Computations”:

For some small organic molecules, we have
found that the basis sets 6-31++G(D,P) and AUG-cc-pVDZ give almost identical results
(protonation energies of 16 amide-containing molecules computed with wB97XD/6-31++G(D,P) and wB97XD/AUG-cc-pVDZ methods correlate with R= 0,99966; this difference
is almost negligible for our applied tasks). In contrast to the results
reported in the aforementioned paper, the total energies computed with wB97XD/AUG-cc-pVDZ
method are 3-30 kJ/mol lower than the energies computed with wB97XD/6-31++G(D,P).

At the same time, with the basis set AUG-
cc-pVDZ the computation time was 3-6 times higher than with the 6-31++G(D,P)
basis set. So, the 6-31++G** basis set should be still considered good enough.

It is usually considered that the computation
of anions or significantly electronegative atoms (which show big negative Mulliken
charge) requires the use of diffuse functions (“++” for 6-31G or “aug” for cc-pVnZ).
However, in the paper [8] this conclusion is criticized to a significant
extent. The authors write:

“We
conclude that the use of diffuse functions for calculating geometrical
parameters for PAH anions in general is unnecessary and does not improve the
calculated results significantly. Energy calculations are affected in much the
same way.”.

As the authors write, the only case when the
diffuse functions are important are the computations of absolute values of
chemical shifts; however, in most cases, when the experimental data are
available, it is no necessary to obtain their absolute values as the
correlations between the computed and experimental values can be built instead.

On the other hand, D. Truhlar who investigated the use of diffuse functions writes here:

"How should one add diffuse functions to the basis set? Diffuse functions are known to be critical in describing the electron distribution of anions (as discussed in my book), but they are also quite important in describing weak interactions, like hydrogen bonds, and can be critical in evaluating activation barriers and other properties."

The Truhlar group recommends using the "jun-" basis sets (see below).

One more source of information is the review "Basis sets in quantum chemistry" by C. David. Sherill. The author writes in this review about the diffuse functions:

Our knowledge of the subject
and our personal experience says that the diffuse functions indeed should be
used when calculating anions. We have computed the energies of deprotonation of
12 carbon acids (with PCM solvation model), both with diffuse functions and
without them (wB97XD/6-31++G(D,P) method and the wB97XD/6-31G(D,P) method), and
the values calculated by the first method correlate much better with
experimental PKa values than the values computed without diffuse function (the
correlation coefficients R are correspondingly 0,99522 for wB97XD/6-31++G(D,P)
and 0,98884 for wB97XD/6-31G(D,P)).

Some
recommendations concerning the choice of basis sets can be found on Orca input library:.
These recommendations are:

- Rule of thumb: Energies and geometries are
usually fairly converged at the DFT level when using a balanced polarized
triple-zeta basis set (such as def2-TZVP) while MP2 and other post-HF methods
converge slower w.r.t. the basis set. Ab initio methods are much more basis set
sensitive than DFT methods

- Stick with one family of basis sets that is
available for all the elements of your system. Mixing and matching basis sets
from different families can lead to problems.

- Calculations on heavy elements can either be
performed using an all-electron approach or effective core potentials (ECPs).

Here is a picture from the Orca input library:

So, it
seems that diffuse functions are really important for computing electron affinities.

As far as we know, usually it is not needed
to use a larger basis set than cc-pVTZ with DFT: further increasing basis set size
will not improve the accuracy of the computation. In contrast, this is not true for ab initio
computations, which will benefit from using larger basis sets, such as cc-pVQZ,
cc-pV5Z, etc.

Some papers,
in which the results of DFT computations are compared to those of ab initio
methods and to the experimental data, conclude that DFT performs not worse (or even slightly better) [10, 11, 12]. This is caused by employing modest
basis sets (not larger than cc-pVTZ) in these papers.

So, the choice between DFT or ab initio
methods depends on which properties are calculated and what accuracy is
required.

The larger the basis set, the more difficult
the SCF convergence is (especially if diffuse-augmented basis sets are used). We recommend to always specify SCF=XQC in GAUSSIAN input files. With this keyword, the scf is firstly converged using the default DIIS algorithm, and if the convergence is not achieved, Gaussian switches to more reliable and costly quadratically convergent SCF procedure.

Ref. [9] describes the role of diffuse
functions in computations. It is known, that for many tasks using the diffuse
functions will not lead to significant increase of computational accuracy, but
will increase the cost of the calculation; besides that, using the diffuse
functions can lead to SCF convergence problems and can increase the basis set
superposition error (BSSE). The authors write: “We conclude that much current
practice includes more diffuse functions than are needed. Often, better
accuracy could be achieved if the additional cost were invested in higher-ζ
basis set or more polarization functions.”

The popular basis set family cc-pVnZ (of Dunning
and co-workers) comprises the diffuse functions, if “aug-” prefix is used. The authors notice that
chemists usually utilize “fully augmented” basis sets, and this may not be
optimal for large molecules. For example, the cc-pVTZ basis set for methane has
s, p, d, and f functions on C and s, p, and d functions on H; aug-cc-pVTZ
contains diffuse s, p, d, and f functions on C and diffuse s, p, and d functions
on H atoms.

In contrast, the earlier “plus” basis sets
originally systematized by Pople and co-workers contained only diffuse s and p functions
on non-hydrogen atoms and no diffuse functions on hydrogen atoms. In Ref. [9]
this is called “minimal augmentation”. The maug-cc-pVTZ basis set retains the
diffuse s and p functions on carbon with the exponential parameters optimized
for the aug case but deletes all other diffuse functions.

So, the authors (Truhlar et al.) conclude that using the
minimal augmentation is usually more optimal than using the full augmentation (particularly
with DFT). The authors recommend the so-called “calendar” basis sets, in
particular the “jun” level of augmentation – for example, the jun-cc-pVTZ set
is recommended in comparison to aug-cc-pVDZ or cc-pVTZ. When increasing the
zeta number in Dunning basis sets (i.e. switching from cc-pVDZ to cc-pVTZ, then to cc-pVQZ, etc), augmentation becomes less important, and using the “calendar”
basis sets provides a more efficient sequence of basis sets (than unaugmented, minimally
augmented, or fully augmented sets) for basis set extrapolation to the complete
basis set limit. We know, however, that many researchers have criticized the approach proposed by the authors.

Anyway,
density functional theory is a “black box”. Look at this picture from Ref. [13]:

Our comment
on this picture:

First and
second points: In contrast to ab initio methods, DFT is not hierarchical. Ab initio
(non-empirical) methods are hierarchical: this means that if we increase basis
set size, level of taking into account the electronic correlation (excitation
rank), and possibly the level of taking into account the relativistic effects
(for heavy elements), we approach the exact solution (within the Born–Oppenheimer
approximation). More specifically, if we go, e.g., through CCSD/cc-pVDZ -> CCSDT/cc-pVDZ -> CCSDTQ/cc-pVDZ -> CCSDTQ5/cc-pVDZ, etc., the
results of the computation systematically approach some limit; if
we go through CCSD/cc-pVDZ ->
CCSD/cc-pVTZ -> CCSD/cc-pVQZ -> CCSD/cc-pV5Z -> CCSD/cc-pV6Z,
etc., the results systematically approach the complete basis set (CBS) limit. For the first row, the improvement can be non-monotonic,
while for the second case the improvement seems to be always monotonic.

So, we can verify the accuracy of an ab initio method by comparing its results with the results of a higher level computation. For DFT, this possibility is much less available.

So, we can verify the accuracy of an ab initio method by comparing its results with the results of a higher level computation. For DFT, this possibility is much less available.

The points
mentioned below are mostly our private opinion, maybe not fully right.

As far as
we know, DFT is often used to “confirm” an experiment. This means that if the
experiment and a DFT computation lead to similar conclusions, this increases
the reliability of the investigation. On the contrary, if the experiment and
the DFT calculation give different results, this can be either a discovery or a
failure (inaccuracy of the computation, or maybe the experiment).

Speaking of “confirming” an experiment, it
should be noted that this approach is only good with an independent experiment.
We know some cases when the experiment was “adjusted” for better agreement with
the computation (both at DFT and ab initio levels).

As mentioned above, it is a good practice to
perform the computation with several different DFT functionals, to ensure that
they all give the same results. And as far as we know, some researchers, being
not honest enough, meaningly avoid using more than one functional, because if
different functionals give contradictory results in their work, this makes this
whole work less “publishable”.

Here you can
read an ironical essay “Obituary : Density Functional Theory. 1927-1993”:

The author claims that the density functional
theory in current implementation is not a mathematically correct approach:

“The Hohenberg-Kohn argument is what
mathematicians call an existence proof, as opposed to a constructive proof.
That is, although we now know that, *in
theory*, DFT can extract as much information from r(r) as her brother can
from Y
( r 1, r 2, ... , r n) , no-one knew how to dress her so that
she could achieve this *in practice*.
All quantum mechanical theories are created equal, but some are more equal than
others.”

The hybrid functionals, which appeared in
1993, are even more unreliable and not correct from the theoretical point of
view; in other words, using such functionals may be a kind of “shamanism”, or maybe
even “scientific charlatanism”. The author thinks that the density functional
theory finally died (we should add, it died as a well-grounded scientific
theory) in 1993, after the spreading of hybrid functionals.

On the other hand, in Ref. [13] the author states the following:

"I believe that a fundamental principle underlies the success

of DFT, which is that local approximations are a peculiar type of *semiclassical* approximation to the many-electron problem. For the last 6 years, with both my group and many collaborators, I have been trying to uncover this connection, and make use of it. The underlying math is very challenging, and some must be invented."

The "DFT shamanism" can exist in the following form: if different functionals are applied to the same object, the user may select any results consistent with experimental data (even the latter are invalid or erroneous) and explain them. We suggest calling such practive "DFT quackery".

In Ref. [13] the following is proposed: "Users should stick to the standard functionals (as most do, according to Fig. 1), or explain very carefully why not."

Here is a picture from Ref. [13]:

A fragment of the paper [13]:

"XII. THE FUTURE

So, where does this leave us? It is clearly both the best and worst of times for DFT. More calculations, both good and bad, are being performed than ever. One of the most frequently asked questions of developers of traditional approaches to electronic structure is: “When will DFT go away?.” Judging from Fig. 1, the answer is clearly no time soon. Although based on exact theorems, as shown in Fig. 2, these theorems give no simple prescription for constructing approximations. This leads to the many frustrations of the now manifold users listed in Table I.Without such guidance, the swarm of available approximations of Fig. 3 will continue to evolve and reproduce, perhaps ultimately undermining the entire field. But I expect that some of the many excellent ideas being developed by the DFT community will come to fruition, i.e., produce new and more general standard approximations, well before that happens."

[3]
S.S.Leang, F.Zahariev, M.S.Gordon, J.Chem.Phys., 136, 104101 (2012)

[4]
G.Garcı´a, C.Adamo, I.Ciofini, Phys. Chem. Chem. Phys., 2013, 15, 20210--20219

[8]
Calculations of PAH anions: When are diffuse functions necessary? Noach
Treitel1, Roy Shenhar, Ivan Aprahamian, Tuvia Sheradsky and Mordecai
Rabinovitz. P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 1 1 1 3 – 1
1 2 1

[10] Do Practical Standard Coupled Cluster Calculations

Agree Better than Kohn–Sham Calculations with

Currently Available Functionals When Compared

to the Best Available Experimental Da...

Article in Journal of Chemical Theory and Computation · May 2015

Impact Factor: 5.5 · DOI: 10.1021/acs.jctc.5b00081

[11] On the dissociation energy of Ti(OH,)+.

An MCSCF, CCSD(T), and DFT study

A. Irigoras, J.M. Ugalde, X. Lopez, and C. Sarasola

Can. J. Chem. 74: 1824-1829 (1996). Printed in Canada / Imprimt au Canada

[13] J. Chem. Phys. 136, 150901 (2012). Perspective on density functional theory. Kieron Burke.

[14]

Jensen, Stig Rune; Saha, Santanu; Flores-Livas, José Abdenago; Huhn, William; Blum, Volker; Goedecker, Stefan; Frediani, Luca, 2017, "GGA-PBE and hybrid-PBE0 energies and dipole moments with MRChem, FHI-aims, NWChem and ELK", doi:10.18710/0EM0EL, UiT Open Research Data Dataverse, V3

[14]

Jensen, Stig Rune; Saha, Santanu; Flores-Livas, José Abdenago; Huhn, William; Blum, Volker; Goedecker, Stefan; Frediani, Luca, 2017, "GGA-PBE and hybrid-PBE0 energies and dipole moments with MRChem, FHI-aims, NWChem and ELK", doi:10.18710/0EM0EL, UiT Open Research Data Dataverse, V3

At this
page we are collecting links we find useful in our own research work.

1) Gaussian
Error Messages

Here 26
types of Gaussian error messages are explained (e.g., memory allocation
problems, change in point group or standard orientation, convergence failure,
etc.).

2)
Practical Advice for Quantum Chemistry Computations, by C. David Sherrill.

Here many
simple hints are provided:

- The choice of basis set;

- The choice of ab initio/DFT methods for
different tasks.

The author
writes that standard HF, semiempirical, and DFT techniques are not appropriate
for van der Waals complexes or systems dominated by London dispersion forces. However, Ref. reported that for the compounds under investigation the B3LYP-gCP-D3/6-31G*
method could correctly compute London
dispersion effects (and it does not have the basis set superposition error);

- Hints on the problem of SCF convergence;

- Common hints on imaginary frequencies and
saddle points;

- Hints on optimization with symmetry.

In our
opinion, blogs are usually more interesting source of information for chemists,
than usual papers. Here we have collected some links to such blogs:

And one
more – in Russian:

Sometimes
the Chemcraft users ask me to implement a GUI for creating input files.
GaussView has such a GUI.

I don’t
plan to implement such a GUI in Chemcraft, because I never had the need to use
it in my research work. To create input files for new jobs, I use my archive of
computed jobs; when I need to create a new input file, I take an input file
from this archive and modify it.

You can
download such an archive here:

This archive
contains more than 150 jobs (both input and output files) with different types
of computation. Besides these files, the archive contains text files with
comments. It also contains some examples of interesting computations with
comments, which illustrate the use of quantum chemistry.

This
archive is protected with password; to get the password, you need to purchase
Chemcraft (the password will be shown in the “Help/License information”
window).

I think
that implementing a GUI for creating input files can be even harmful, because
it will give you a false feeling of easy creation of new jobs; but when you
need to create a non-standard job (e.g., a PES scan), this GUI will become useless.

I wrote this statement in our Facebook group, and
two persons fully agreed with my conclusion (none disagreed).
When the
results of quantum chemistry computations are directly compared with
experiment, often quite poor agreement is obtained. However, this agreement
often becomes much better, if a series of homologues is taken and a correlation
is built between the computed and experimental values. Here I present some samples
of such correlations:

1)
Correlation
between QC (T1(1)) and experimental heat of formation for a set of 1800 diverse
organic molecules from NIST thermochemical database (from Wikipedia):

The mean
absolute and RMS errors are 8.5 and 11.5 kJ/mol, respectively.

2) Correlation
between computed and experimental NMR spectra.

We have found
that usually the computed NMR chemical shifts are rather far from the
experimental ones; maybe the physical meaning of the chemical shifts is not
clear enough. At the same time, the computed values correlate well with the
experimental ones

a) Such
correlation for several Shiff bases:

The calculations were performed with B3LYP/6-311G(D,P) method, but the B3LYP functional is considered obsolete at the moment. You should better use PBE, wB97XD or B3LYP-D3 instead. 6-311 G is not a good basis set too, you should better use, e.g., cc-pVDZ.

b) A bodipy molecule:

b) A bodipy molecule:

A similar
correlation can be obtained for H1 chemical shifts (several bodipy molecules):

I have
found that a good correlation is usually obtained for C13 chemical shifts; for
H1 chemical shifts the correlation is rather good too, but only for hydrogen
atoms attached to carbons.

c) One more correlation from this site:

http://cheshirenmr.info/

c) One more correlation from this site:

http://cheshirenmr.info/

3) An
important correlation can be obtained between computed energies, or maybe Gibbs
energies, and experimental reaction constants.

a) Here is
one such correlation for a set of 9 carboxylic acids:

The
energies were computed at PCM wB97XD/6-311++G(DP) level (the solvent is water),
with two water molecules added to the model for taking into account the
specific solvation.

The
correlation between QC energies and experimental reaction constants is based on
the assumption that the entropy contribution to the Gibbs energy within a row
of compounds is small relative to the energy contribution (if not, one can
compute the Gibbs energies as well).

b) Some
more correlations between the energy and PKa for 5 sets of compounds, taken from
paper [1]:

The
theoretical constants were calculated from the Gibbs energies of deprotonation
computed at PCM B3LYP/6-311+G(d,p) level (the solvent was DMSO).

4) A
similar correlation can be obtained between the computed energies and
experimental rate constants. Here are some samples from our work:

a)

I have studied the reaction of C-Cl bond
elimination of some anion radicals:

....

The computed energies of the C-Cl bonds correlate with the experimental rate constants of the bond elimination reaction:

b)

I have studied the reaction of substitution of
alcohol ligands by imidazole using QC and experimental methods:

Apart from methanol, the data for other
alcohols were also obtained:

The alcohol substitution was studied using
electronic spectra. The experiment showed that this reaction has two stages,
each stage having its own rate constant. Then I computed the energies
Cr-Alcohol, and plotted the graph “Computed energies vs. experimental constants
of correlation (first stage)”:

Note that
in both cases no solvation modeling was used; this means that if we investigate
the tendency within a series of homologues, the accuracy of a simple quantum
chemistry computation (gas phase modeling) is sufficient to make important
conclusions.

5) We have found a correlation between the computed and experimental components of polarizability tensor for some Shiff bases:

6) For computation of electronic spectra using the TDDFT method, the correlation seems to be worse:

a) [2]:

b) [3]:

c) [4]:

d) [7]

FIG. 7. Accuracy plots for TDDFT calculated excitation energies for metaGGAs: (a) VS98, (b) PKZB, (c) TPSS, (d) M06-L, (e) TPSSm, (f) revTPSS, (g) TPSSh, (h) M05, (j) M06, (k) M06-2X, (l) M06-HF, (m) M08-HX, and (n) M08-SO. Points above the line indicate positive errors while points below the line indicate negative errors.

e) [8]

f) For some Bodipy molecules, the correlation seems to be better []:

7) Here is
the correlation between computed and experimental collision diameters of some
molecules (mostly organic):

The
experimental collision diameters were taken from [5,6]. The computed ones were
obtained with Chemcraft: firstly the molecular geometries were obtained at
B3LYP/6-31G(D,P) level (again, we don’t recommend using this method, we just don’t
want to repeat the jobs with another level of theory), and then the diameters
were computed by Chemcraft via “Tools/Calculate collision diameters” menu item.

8) The
following graph should not be called a “correlation”, but it illustrates some
practical use of quantum chemistry. The X values correspond to the anisotropy
of molecular polarizability of some nematic liquid crystals (Shiff bases), the
Y values correspond to the temperatures of phase transitions (nematic-isotrope).
The first ones were computed with DFT, the latter (experimental values) were
taken from literature:

The symbols above the points represent fragments of molecules which vary among series.

This correlation is so poor not because the computation give wrong results; as it can be seen above, the computed components of molecular polarizability correlate well with experimental ones. So, the reason of such bad correlation is the imperfection of this approach (that the thermal stability of liquid crystal depends on their molecular polarizability).

This correlation is so poor not because the computation give wrong results; as it can be seen above, the computed components of molecular polarizability correlate well with experimental ones. So, the reason of such bad correlation is the imperfection of this approach (that the thermal stability of liquid crystal depends on their molecular polarizability).

9)
Vibrational frequencies

We have
computed the vibrational spectra of some simple organic compounds (toluene,
propene, acetone, benzoic acid, etc) using wB97XD/aug-cc-pVTZ method, and
compared the mode frequencies with the experimental values:

The blue
line indicates full theory/experiment match. Some improper attribution of the
bands is possible.

We have
also computed the same frequencies at a lower level (wB97XD/6-31G(D,P)). The
standard deviation turned out to be 29 cm-1 for wB97XD/6-31G(D,P) and 24 cm-1
for wB97XD/aug-cc-pVTZ. The job CPU time with the latter method was 50-100
times higher than with the former method.

Refs:

[1] Sergey
L. Khursana and Mikhail Yu. Ovchinnikova. The pKa theoretical estimation of
C―H, N―H, O―H and S―H acids in dimethylsulfoxide solution. Journal of physical
organic chemistry, 9/24/2014, DOI 10.1002/poc.3371.

[2] Nesrin Tokay, Zeynel Seferoğlu, Cemil Öğretir and Nermin Ertan. Quantum chemical studies on the structures of some heterocyclic azo disperse dyes.ARKIVOC 2008 (xv) 9-20

[3] S. Kawauchi, L. Antonov, Y. Okuno. Prediction of the color of dyes by using time-dependent density functional theory (TD-DFT). Bulgarian Chemical Communications, Volume 46, Special Issue A (pp. 228 – 237) 2014.

[4] Denis Jacquemin, Eric A. Perpe`te, Gustavo E. Scuseria, Ilaria Ciofini, and Carlo Adamo. TD-DFT Performance for the Visible Absorption Spectra of Organic Dyes: Conventional versus Long-Range Hybrids. J. Chem. Theory Comput. 2008, 4, 123-135

[2] Nesrin Tokay, Zeynel Seferoğlu, Cemil Öğretir and Nermin Ertan. Quantum chemical studies on the structures of some heterocyclic azo disperse dyes.ARKIVOC 2008 (xv) 9-20

[3] S. Kawauchi, L. Antonov, Y. Okuno. Prediction of the color of dyes by using time-dependent density functional theory (TD-DFT). Bulgarian Chemical Communications, Volume 46, Special Issue A (pp. 228 – 237) 2014.

[4] Denis Jacquemin, Eric A. Perpe`te, Gustavo E. Scuseria, Ilaria Ciofini, and Carlo Adamo. TD-DFT Performance for the Visible Absorption Spectra of Organic Dyes: Conventional versus Long-Range Hybrids. J. Chem. Theory Comput. 2008, 4, 123-135

[5] H.
Wang, M. Frenklach, Combust. Flame 96, 163 (1994)

[6] R.J.
Kee et al.Chemkin Collection, Release 3.6, Reaction design, Inc., San Diego, CA
(2000)

[7]Sarom S. Leang, Federico Zahariev, and Mark S. Gordon.THE JOURNAL OF CHEMICAL PHYSICS 136, 104101 (2012).

[8] K. Okuno et al. J.Photochem.Photobiol A: Chemistry 235 (2012) 29– 34

[9] J. Chem. Theory Comput. 2014, 10, 4574−4582

[7]Sarom S. Leang, Federico Zahariev, and Mark S. Gordon.THE JOURNAL OF CHEMICAL PHYSICS 136, 104101 (2012).

[8] K. Okuno et al. J.Photochem.Photobiol A: Chemistry 235 (2012) 29– 34

[9] J. Chem. Theory Comput. 2014, 10, 4574−4582

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