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.
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\require{cancel}
\newcommand{\op}[1]{\...
- 44.4k
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 ...
- 4,759
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 ...
- 3,090
9
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 ...
- 2,883
9
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\...
- 1,452
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, ...
- 44.4k
7
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 ...
- 205
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 $\...
- 4,759
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 ...
- 2,130
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 ...
- 10.9k
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
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 ...
- 4,819
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 ...
- 13.2k
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
Accepted
Effective core potential and Gaussian basis set
Using a basis set that is not designed for the effective core potential is not a good idea. The problem is that an ECP is designed to produce the effective potential of core electrons, and an all-...
- 746
3
votes
Spectroscopic constants - explanation
The subscript $e$ means measurements relating to the minimum of the internuclear separation, i.e. at the bottom of the potential energy. Many textbooks do not use the subscript $e$ at all but the ...
- 31.4k
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 ...
- 4,759
3
votes
Accepted
Ab initio method to calculate C-C bond dissociation energy?
This "experiment" is about determining bond dissociation energy.
The general way to solve this isn't like calculating enthalpies of reaction, as I initially thought, but rather through calculating ...
- 191
3
votes
Is density functional theory an ab initio method?
As already answered in the MatterModeling Stack Exchange, I think there is one aspect missing, and here I would like to quote my late PhD supervisor Jaap Snijders.
The most important aspect to know if ...
- 131
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 ...
- 4,759
2
votes
How closely should the energy components of ab initio SCF results at a stationary nuclear configuration preserve the virial theorem?
Originally, I was convinced that the molecular geometry has very limited influence on the virial ratio: only in so far as the effective basis set will change with the geometry as long as nuclei-...
- 7,039
2
votes
How closely should the energy components of ab initio SCF results at a stationary nuclear configuration preserve the virial theorem?
I am posting a second answer rather than editing my first answer basically just because my first answer is wrong, and this answer is just going to present some data and then make the opposite claim of ...
- 13.2k
2
votes
What are the steps of Hartree-Fock Theory?
Yeah, I think it asks you to write the energy as expectation value, vary one orbital and get the Roothan equation.
The Hartree Fock model is the extension of the Hartree model where the wavefunction ...
- 46
1
vote
Is the Hartree-Fock determinant always the minimum energy single Slater determinant solution to a molecular Hamiltonian?
By construction, any determinant $|\chi_{i_1}\ldots \chi_{i_N}\rangle$ where the $\chi_{i_j}$ are distinct solutions of the Hartree-Fock equation $f(x) \chi(x) = \epsilon_i \chi(x)$ will have ...
- 86
1
vote
Is there a rule of thumb to predict when coupled cluster might dip below the variational limit?
Let us begin with the following principle: the CC ansatz always returns an appropriate electronic wavefunction (meaning a combination of Slater determinants). Still, at least in a non-relativistic ...
- 46
1
vote
Ab Initio and Molecular Orbitals
Ab initio means calculations that are strictly from the principles of quantum mechanics. This contrasts with a non ab initio method which can involve parameters that do not arise directly from ...
- 1,394
1
vote
Is coupled cluster variational for two electrons?
Yes,
in the particular case of 2 electrons, CCSD is strictly equivalent to CISD since there can't be any excitation higher that singles and doubles. CISD is the Full-CI of a 2-electron system, so CCSD ...
- 205
1
vote
Building a solid-liquid interface
First, when it comes to periodic boundary conditions, you should make sure that your system does not interact with itself through the boundaries.
A way to check it is to see if the electron density is ...
- 2,883
1
vote
Boys function for Gaussian integrals in ab initio calculations
I published an implementation in C/C++ in http://vixra.org/abs/1709.0304 which uses Gauss-Jacobi quadratures. It is limited to quantum numbers of 130 and to real arguments; a relative accuracy near 1....
- 11
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