15 votes
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Why are correlation consistent basis sets used with DFT calculations?

It is generally recommended not to use a cc basis set with a DFT method (and I guess conversely, a basis set aimed at DFT should not be used with a coupled cluster method). This statement glosses ...
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13 votes
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Why are basis sets needed?

Spatial orbitals $\phi_i$ in modern electronic structure calculations are indeed typically expressed as a linear combination of a finite number of basis functions $\chi_k$, \begin{equation} \phi_i(...
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12 votes
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"NBO diagrams" versus MO diagrams

A molecular orbital diagram is a schematic representation of how we interpret bonding in certain species. It is as much an accurate representation for a specific bonding situation as a Lewis structure ...
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12 votes

Matching a Slater-type wavefunction with a minimal (STO-nG) Gaussian basis set

TL;DR The procedure to represent a Slater-type orbital (STO) as a linear combination of Gaussian-type orbitals (GTO) is outlined in W. J. Hehre, R. F. Stewart and J. A. Pople, J. Chem. Phys. 1969, 51,...
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12 votes
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How to compute 2-electron integral for Hartree-Fock code?

You can also write this down in a similar way as for the one-electron integral. You already had: \begin{equation} \mathbf{S} = \mathbf{D_2}' * \mathbf{S}_{\rm prim} * \mathbf{D_2} \end{equation} ...
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11 votes
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How many basis functions used in STO-3G and 6-31+G** for the water molecule?

Notation ** is just a synonym for (d,p), so that 6-31+G** basis is just a different name of ...
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11 votes
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Computing two-electron integrals with an STO-3G basis set

Actually there is a mistake in the analtical expression in Cook's Book. On his web page he has a pdf with the corrected verison http://spider.shef.ac.uk/ Maybe this solves your problem, but I would ...
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  • 546
11 votes
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How does one compute the number of unique 2-electron integrals for a given basis set?

To find the number of unique $2e^-$ integrals $\left<AB|CD\right>$, it is useful to first find the number of unique $1e^-$ integrals $\left<A|B\right>$. If $n$ is the number of real ...
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11 votes
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How do the def2-SV, def2-SV(P), and def2-SVP basis sets differ?

Def2-SVP has the polarisation functions on all atoms, -SV(P) does not have these functions on the hydrogen atoms and -SV does without them. In future, you can check on the EMSL Basis Set Exchange It ...
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10 votes
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The eigenvector matrix C

$\mathbf{c}_n$ is a vector with $N$ entries (I switched to boldface to indicate - hopefully slightly more clearly - that it is a vector): $$\mathbf{c}_n = \begin{pmatrix}c_{1n} \\ c_{2n} \\ \vdots \\ ...
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10 votes

Coefficients and Parameters for contracted Gaussian basis sets

Take a look at the carbon STO-3G first. It means for each AO, you form it with three Gaussians. For carbon, you have a 1S, 2S and (three) 2P. 5 functions when finished. The top line says you are ...
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10 votes

Why are correlation consistent basis sets used with DFT calculations?

Because in fact it is appropriate. In most cases there is not a huge difference (quality/efficiency) among basis set families. For example Dunning (cc) basis sets work reasonable well for DFT, and ...
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10 votes
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Use of basis set in DFT (Density Functional Theory)

This answer only deals with the most common variety of Density Functional Theory, namely, Kohn-Sham DFT. This is what most people mean by "DFT", but, as noted in the comments, things such as orbital-...
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Is it good practise to mix double and triple zeta basis sets?

It is perfectly fine, and actually quite common, to use big basis sets for the most important atoms (perhaps at the active site of the chemical reaction) and a smaller basis set for the surrounding ...
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9 votes
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Pople Basis Set Abnormality: 3rd row 6-311G

From the Gaussian[1] webpage: 6-311G: Specifies the 6-311G basis for first-row atoms and the McLean-Chandler (12s,9p) → (621111,52111) basis sets for second-row atoms [McLean80, Raghavachari80b] (...
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  • 1,251
8 votes
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Can PBE (and LDA) actually be a better choice sometimes?

Can PBE (and LDA) actually be a better choice sometimes? Of course, they can. This is in fact one of the major problems with DFT: there is no systematic way of improving a functional, so we never ...
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8 votes
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Boys function for Gaussian integrals in ab-initio calculations

I am not aware of any existing Fortran code for direct numerical quadrature of this problem, but it is worth pointing out that Mathematica can perform this integral symbolically: ...
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8 votes
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How to choose the best method and basis set for a calculation in computational chemistry?

The experimental equivalent of your question would be: what kind and level of impurity am I going to accept in my experiment? In terms of basis sets: in principle you keep increasing the complexity ...
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  • 1,355
7 votes

Boys function for Gaussian integrals in ab-initio calculations

I know this is an old question, but I would like to give a small comparison regarding efficiency when evaluating the Boys function $F_n(x)$. Below are some implementations (in Julia) with simple ...
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7 votes
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Why large basis sets give better approximations to the exact solution of the Schrödinger equation?

The statistics analogy may not be applicable, but it illustrates what goes on in my head. The overfitting analogy is indeed not applicable here. It is a totally different and unrelated phenomenon. ...
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7 votes

Computing two-electron integrals with an STO-3G basis set

My advice is to implement the Obara-Saika recurrence formulae that are outlined in "Molecular Electronic-Structure Theory" by Helgakar, et al. I would stick with Cartesian functions, since a) they are ...
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6 votes

Boys function for Gaussian integrals in ab-initio calculations

The Boys function is $F_n(x)$ a special case of the Kummer confluent hypergeometric function $M(a,b,x) = {_1}F_1(a,b,x)$, which can be found in many special function libraries, such as ...
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  • 2,040
6 votes

How to compute 2-electron integral for Hartree-Fock code?

As was mentioned in the comments, this amounts to the same fundamental operation as the AO-to-MO transformation; they are both 4-index transformations. (...) each contracted integral $(\mathbf{ab}|\...
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5 votes

Largest system studied by full CI

FCI of N2 with about 10^10 CSFs must be the largest such calculation... Ref: A full-configuration benchmark for the N2 molecule, Elda Rossi, Gian Luigi Bendazzoli, Stefano Evangelisti, Daniel Maynau,...
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5 votes

Why are basis sets needed?

This answer, I hope, complements those earlier ones and give some little explanation as to how the basis set calculation works. As pointed out already it is not necessary to use a basis set to ...
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5 votes

Why are basis sets needed?

The idea of using basis (in general sense, not just basis set) in electronic structure theory is due to the fact that we can't solve the wave function of a system analytically except those with only ...
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5 votes

Computing two-electron integrals with an STO-3G basis set

My suggestion would be to use another existing code and run the calculation. For example, if I do an HF/STO-3G calculation on $\ce{H2O}$, I get: $$E_\mathrm{H_2O}=-74.9659011\:\mathrm{a.u.}$$ I don'...
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4 votes
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An alternative basis set for analytical computation of two electron integrals

A few things come to mind: 1) my understanding is that (ab|cd) in a gaussian basis is exactly solved for arbitrary "angular momenta" using recurrence relations such as the Obara-Saika method. The O-S ...
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