9
votes
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 ...
- 33.6k
7
votes
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 ...
- 18k
6
votes
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 ...
- 33.6k
6
votes
Constrained optimisation on a hypersphere
I'll propose a slightly different Lagrangian expression:
$$ L = E' + g^T \Delta x + \frac{1}{2} \Delta x^T H \Delta x + \frac{1}{2} \gamma \Delta x^T \Delta x - \frac{1}{2} \lambda (p^T p - k). \tag{1}...
- 2,673
5
votes
Accepted
How to Derive the Kong-Chakrabarty Mixing Rules
I will focus on deriving equations (3) and (4) from equations (6) and (7). In brief: we use equation (7) to derive $r_j$ as a function of $r_i$, and then differentiate (6) in $r_i$ to derive the ...
- 2,673
5
votes
Is the following description talking about the simulation box or the boundary condition?
It's not talking about either, although it is related to those. They are restraining their system by adding a harmonic potential at the "boundary", which will prevent atoms from escaping.
A ...
- 6,647
5
votes
Accepted
How is the equation for the position of a virtual site derived?
The formula (1) in the question:
$$
\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}}...
- 2,673
4
votes
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 ...
- 2,762
4
votes
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 ...
- 18k
4
votes
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 ...
- 18k
3
votes
Accepted
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 ...
- 18k
2
votes
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 ...
- 33.6k
2
votes
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 ...
- 18k
2
votes
Accepted
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 ...
- 33.6k
2
votes
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 ...
2
votes
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 ...
- 2,673
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 ...
- 18k
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 ...
- 33.6k
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^\...
- 33.6k
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 ...
- 3,084
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