# Tag Info

### Inconsistencies in a famous point group table

After hours of conversation with three participants including me, I can make the following conclusions. Answer to the question It's likely an unintentional "error" in the publication. In ...
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### Are there non-antisymmetric solutions to the electronic Hamiltonian?

So, your question is "are the solutions of the Schrödinger equation guaranteed to be anti-symmetric functions, or is this an ad hoc assumption resulting from knowledge of the anti-symmetry ...
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### For one atom, what is the correct point group?

When choosing the point group, a system with a single nucleus (e.g. a single atom) is considered to be spherically symmetric, so its point group is $K_h$ in Schoenflies notation, in which K stands for ...

### Are there non-antisymmetric solutions to the electronic Hamiltonian?

There are several things to notice here. First, the Hamiltonian you wrote is not a completed definition of an operator, since it lacks boundary conditions. This means that there's no eigenproblem yet. ...
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### Speed of atom from kinetic energy of molecule

What is the kinetic energy of a molecule? There is not just one type of kinetic energy when we have a composite system (made up of more than one particle, as in the case of a molecule). For example, ...
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### How do I get the energy, if I have the wavefunction?

"For a known wave function, should I not be able to determine the energy?" The wavefuncton is an eigenfunction of the Hamiltonian, and the energy is a corresponding eigenvalue of the same ...
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### How is the equation for the position of a virtual site derived?

The formula (1) in the question:  \mathbf{r}_s = \underset{\text{term A}}{\mathbf{r}_i} + \underset{\text{term B}}{d \cos\theta\, \frac{\mathbf{r}_{ij}}{|\mathbf{r}_{ij}|}} + \underset{\text{term C}}...
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### Is the following description talking about the simulation box or the boundary condition?

It's not talking about either, although it is related to those. They are restraining their system by adding a harmonic potential at the "boundary", which will prevent atoms from escaping. A ...
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### Is the electron-electron interaction to blame, for the added complexity of using "orbitals" for an N-electron system?

Interpreting the question For a 1-electron system, wavefunctions and orbitals are the same thing. For a 2-electron system, or any N-electron system with N>1, we can use "orbitals" to ...

### What is the computational scaling of DFT energy vs gradient vs Hessian?

Energies An excellent answer to this question was provided here, and arose immediately with this Google search. Numerical gradients Derivatives of energies with respect to a nuclear coordinate can be ...

### Are there non-antisymmetric solutions to the electronic Hamiltonian?

It depends on what you mean. If your Hamiltonian is defined on $H_N:=\otimes^N \mathfrak h$, the $N$-fold tensor product of the single-particle Hilbert space $\mathfrak h$, then actually under quite ...
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### Evaluating analytic gradients for overlap integrals

You don't have to write special code for derivative integrals. Since you know that the Cartesian Gaussian basis functions are of the form $\chi_x = (x-x_0)^l \exp[-\alpha (x-x_0)^2]$ (same for the ...
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### Why does the C6z operator have 6 eigenvectors in this paper?

The paper appears to have an error. When a $C_6$ operator acts on an atom's (x,y,z) coordinates, the operator's matrix representation is the 3x3 matrix that you correctly provided in your question ...

### How do I get the energy, if I have the wavefunction?

UPDATE: I didnt read your post carefully enough. My answer is irrelevant. In your comment above you said I guess what i meant was that if I have an arbitrary state eigenfunction (approximated as the ...
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### Are there non-antisymmetric solutions to the electronic Hamiltonian?

Update: I carelessly misunderstood the specific question I replied to as asking about the kinetic energy operator only. My answer isn’t applicable here, but I’m gonna leave it for reference unless ...
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### How is the equation for the position of a virtual site derived?

I have posted the same question in Mathematics StackExchange and here is the reply. Suppose that $d=|\mathbf{d}|$ and $\mathbf{r}_{ij}\ne \mathbf{0}$. Then in the plane of the other three particles ...

### Cubic spline interpolation through a series of images

The whole point of splines is that, as piecewise polynomials, they are cheap to interpolate. So here's how to numerically re-parametrise a spline by arc length: Form a fine grid of the prior ...
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### What is the real form of p-type gaussian basis functions?

After testing my own code it appears to be the case that each 2px, 2py, and 2pz gets its own contracted basis function, each of which share the same exponents and contraction coefficients. Proceeding ...
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1 vote
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### Correct expressions for one-center Gaussian radial two-electron integrals

Upon further examination, although the recursion relation used to evaluate the $E$ functions given in the paper are wrong, it turns out that the equation in terms of the binomial coefficients is ...
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