31
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
$$
D(...
- 7,378
15
votes
Accepted
Why are correlation consistent basis sets used with DFT calculations?
It is generally recommended not to use a cc basis set with a DFT method (and I guess conversely, a basis set aimed at DFT should not be used with a coupled cluster method).
This statement glosses ...
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13
votes
Is coupled cluster variational for two electrons?
No. The reason for this is not to be found in the excitations, but in the evaluation of the method, i.e. the working equations.
$$%Introducing some shortcuts
\require{cancel}
\newcommand{\op}[1]{\...
- 43.7k
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 ...
- 27.6k
11
votes
Accepted
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 ...
- 546
11
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 ...
- 18.8k
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 ...
- 4,679
10
votes
Accepted
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 ...
- 7,378
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 ...
- 1,967
9
votes
Accepted
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 $\ce{Na}$ ...
- 18.8k
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, ...
- 43.7k
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 ...
- 3,050
8
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\...
- 1,377
8
votes
Accepted
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 ...
- 1,394
8
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 ...
- 2,853
8
votes
Accepted
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:
...
- 3,924
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 ...
- 3,924
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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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 $\...
- 4,679
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 ...
- 2,090
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'...
- 27.6k
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 ...
- 214
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 ...
- 10.5k
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.
- 1,332
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 ...
- 4,789
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 ...
- 12.9k
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 ...
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 ...
- 4,679
3
votes
Accepted
Why is the active space for the dinitrogen cation defined this large in my example?
The active space is a truncation of the full CI space. Hence, including more virtual orbitals will lower the energy and eventually approach the FCI limit. The larger the active space, the more ...
- 4,679
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