30 votes
Accepted

Is density functional theory an ab initio method?

First note that the acronym DFA I used in my comment originates from Axel D. Becke paper on 50 year anniversary of DFT in chemistry: Let us introduce the acronym DFA at this point for “density-...
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25 votes
Accepted

What are typical runtimes for CASSCF calculations?

There is nothing trivial about MCSCF calculations because it is hard to predict a priori how long a calculation will take. There are well-defined equations for calculating how many determinants $$ D(...
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15 votes
Accepted

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

Is coupled cluster variational for two electrons?

No. The reason for this is not to be found in the excitations, but in the evaluation of the method, i.e. the working equations. $$%Introducing some shortcuts \require{cancel} \newcommand{\op}[1]{\...
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12 votes

Is density functional theory an ab initio method?

The convention used by many is that ab initio refers solely to wave-function based methods of various sorts and that first principles refers to either wave-function or DFT methods with little ...
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11 votes
Accepted

How does optimizing the molecular orbital coefficients in CASSCF improve its multi-reference capabilties?

I think you are maybe confusing how dynamical and static correlations are treated with different method. Also CASSCF by itself is not a multi-reference method. CI in general is able to describe both ...
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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
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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Initial guess for Unrestricted Hartree-Fock calculation

When $N_{\alpha} = N_{\beta}$, a restricted solution of Roothaan equations is a solution to the unrestricted Pople-Nesbet equations. This restricted solution always exists and necessarily results if ...
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10 votes
Accepted

Gaussian09 vs home made Hartree-Fock implementation

Diagonalization of the core Hamiltonian provides usually not the best guess for the SCF procedure to say the least, and thus, by default Gaussian uses a more sophisticated guess obtained by ...
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9 votes

Proof of Brillouin's theorem using the diagonality of the Fock matrix

Your question actually contains two linked inquiries. The proof itself depends on the nature of the Fock-operator to which I'll have a few words afterwards. For the proof itself it is only important, ...
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9 votes

How does optimizing the molecular orbital coefficients in CASSCF improve its multi-reference capabilties?

The distinction between static and dynamic correlation is not well-defined.1 The distinction is only sensible with respect to a single-particle picture, i.e. viewing the many-electron wavefunctions as ...
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  • 2,992
9 votes
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What is the reason for including excited states in the wave function in post-Hartree Fock methods?

I think that here it is not accurate to say "starting from the Hartree-Fock picture", instead of it, I find better to say "starting from the Hartree-Fock method". When this method is carried out we ...
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9 votes
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Ab initio effective potentials

First off, I would like to note that you wrongly interpreted the very first equation. Below I quote the relevant part of the paper: In the Hartree-Fock (HF) approximation for, say, the $\ce{Na}$ ...
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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
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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  • 3,905
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

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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7 votes

Why is Coupled Cluster not variational?

The most popular versions of CC are not variational because they have $\Psi_1 \ne \Psi_2$ in this type of estimate for the energy: $$ \frac{\langle\Psi_1| \hat{H} |\Psi_2\rangle}{\langle\Psi_1| \Psi_2\...
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  • 1,327
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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  • 2,030
6 votes

Proof of Brillouin's theorem using the diagonality of the Fock matrix

The Hartree-Fock method minimizes the energy by diagonalizing the Fock matrix, therefore by definition we have \begin{equation} \langle \chi_i|f|\chi_j\rangle = 0, i \neq j \end{equation} where $\...
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  • 4,514
6 votes

Is coupled cluster variational for two electrons?

My previous answer was downvoted (-3!), but I maintain that in the particular case where there are only two electrons, CCSD is equivalent to CISD and Full-CI. If the discussion was about asking if for ...
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5 votes

Is coupled cluster variational for two electrons?

In the most general case, CC can be understood simply as a prescription for a trial wave function (ansatz) that uses the exponential excitation operators. This ansatz can be then optimized ...
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  • 214
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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5 votes
Accepted

Spectroscopic constants - explanation

You can find plots and further explanations online (as I easily did). This is a homework-type question, yet I do feel that the information request for diatomic molecular spectroscopic constants ...
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4 votes

What are typical runtimes for CASSCF calculations?

It seems increasing the active space helped make the CASSCF calculation converge. I've had success with increasing the number of active orbitals from 8 to 10. It only took an hour or so.
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  • 1,274
4 votes

What's a good measure of the Eigen-ness of a wavefunction?

$\hat{F}\psi_i=\varepsilon_i \psi_i \implies \langle\phi_k|\hat{F}|\psi_i \rangle = \varepsilon_i\langle\phi_k|\psi_i \rangle$. So the Fock matrix $F_{ki}$ can be approximated by the product of ...
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  • 4,759
4 votes

How closely should the energy components of ab initio SCF results at a stationary nuclear configuration preserve the virial theorem?

I hope I am not mistaken about this, but if I'm wrong then I'll learn so no big deal. I believe this is a result of the fact that the electrons do not experience a true $r^{-1}$ potential due to ...
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4 votes

Effective core potential and Gaussian basis set

Sure, it can be valid physically. You can use the full-electron basis set, like 6-31G*, and the ECP with associated basis set, like Lanl2dz, for instance, in calculations of transition metal compounds ...
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3 votes

Potential energy surface when spin changes

Dissoziation is a typical multi-reference problem, where single-reference methods like Coupled-Cluster usually fail. Therefore CASSCF+MRCI would be the better approach here anyway. If you have a ...
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