# 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 ...
Accepted

### Numerical Evaluation of Hessian?

Finite differences Let's take a general $2n+1$ point central finite difference rule with uniform grid spacing $$f'(x) \approx h^{-1} \sum_{i=-n}^{n} w_i f(x+ ih),$$ such as two-point central finite ...

### What is the X in Almlöf and Taylor's "Unified treatment of energy derivatives?"

Question "Jan Almlöf and Peter R. Taylor (link) provides little further detail, by defining U=exp(X), but not providing details how X can be calculated here." Answer $X$ is literally ...

Accepted

### Estimate the time between different residues?

Let the centre of mass of each residue be denoted as $r_i$ and is evaluated at every frame. Let the centre of mass of the combined system be $r_c$ where c denotes combined. You can evaluate the ...

### 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 ...
Accepted

### Decay rate of DSD-PBEPBE-D3BJ

I guess the OP is referring to the asymptotic potential which is -1/r with the optimized effective potential (OEP) but which decays exponentially with density functionals as well as Hartree-Fock ...
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### Molecular integrals in spherical harmonics?

Molecular integrals aren't typically computed in spherical harmonics. What you do instead is to compute the integrals in the Cartesian representation, where they are separable, and then transform to ...

### What is the curve fitting model used for the "Qubit™ Protein Assay Kit"?

This is Fig 3 of the PDF that you linked to us, as pointed out in the comment by Anyon. The captio to Fig 3 is: "Figure 3. The curve-fitting algorithm used to determine concentration in ...

### Which specific perturbation do we consider applying to the potential when defining the energy derivative of the log derivative?

You should not be thinking about a specific perturbation operator. The key thing here is that the orbitals are Kohn-Sham eigenfunctions, and that already reveals everything that is needed. Still, it ...
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### Understanding the complexity of geminal-based wavefunctions

"Why does the paragraph after expression (10) says that AGP has a complexity of O(K^2) which contradicts its own sentences just after expression (5) about having binomial complexity? Expression ...

### 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 ...
1 vote
Accepted

### 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 ...
1 vote

### What is the meaning of a "free energy per unit surface area" vs "pressure" plot?

The graph does show that at high pressures the $\Delta G$ per surface area values are lower, which would usually indicate stability. I agree with you that as the pressure goes lower, the stability ...
1 vote

### Why is strain rate used instead of absolute strain for modelling stress relaxation of a viscoelastic material using the Maxwell model?

If we integrate both sides of: $$\frac{d\epsilon}{dt} = \frac{d\sigma}{dt} \cdot \frac{1}{E} + \frac{\sigma}{\eta} \tag{1}$$ with respect to time, we get: \int_0^t \frac{d\epsilon}{dt^\prime} dt^\...
1 vote

### Inverse Matrix Calculation

This sounds like you are doing something wrong. Even in a non-orthogonal basis the diagonal $\mathbf S$ matrix has the identity matrix in the diagonal. There could be a number of reasons why this ...

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