[CP2K-user] [CP2K:19463] Computing MO coefficients using CP2K outputs

['Maximilian Franz-Xaver Dorfner' via cp2k]

Hi,
although I am no CP2K developer, I may can contribute to your answer. I
cannot comment your programm, since I have not looked deeply into it.

To my impression benzene is a bad choice, when it comes to reproducing the
mo coefficients, as it hast lots of degeneracies, which reflect the
symmetry. At degeneracies the standard eigensolver routines converge to
some eigenvectors, but at say a twofold degeneracy the linear combination
of to eigenvector is (analytically) again an eigenvector. This implies
that, without an additional contstraint, it is very unlikely to reproduce
all the coefficients, as the the CP2K solver may converge to a rotated
solution compared to yours.

Best regards,
Maximilian Dorfner





mshakiba.k... at gmail.com <mshakiba.kerman.iran at gmail.com> schrieb am Mo., 6.
Nov. 2023, 03:28:

> Dear CP2K developers,
>
> Hi, For educational purposes, I wanted to show how CP2K generates the MO
> coefficients. I've selected benzene with a SZV basis and the convergence
> limit is `1.0e-8`. Then, I printed the overlap (S), Kohn-Sham (K), and
> density matrices (P) in my input (using `&AO_MATRICES` section) and parsed
> them into Python. I used the same procedure as in CP2K paper
> <https://www.sciencedirect.com/science/article/abs/pii/S0010465505000615> as
> follows (I have attached the image as well):
> ```
> # Cholesky decomposition of the Overlap matrix
> U = np.linalg.cholesky(S).T
> # U^1/2 was also tested
> # U = scipy.linalg.fractional_matrix_power(S, 0.5)
> # Printing of the U^T * U to make sure the decomposition is correct
> print(np.dot(U.T, U))
> # Computing U^-1 and U^T -1
> U_inv = np.linalg.inv(U)
> UT_inv = np.linalg.inv(U.T)
> # Computing K'
> K_prime = np.linalg.multi_dot( [UT_inv, K, U_inv] )
> eigenvalues, eigenvectors = np.linalg.eig(K_prime)
> sorted_indices = np.argsort(eigenvalues)
> c = eigenvectors[:,sorted_indices]
> # Back transformation
> first_eigenvector = np.dot(U_inv, c[0])
> ```
> Surprisingly, when I compare the outputs, I don't get the same
> coefficients as is printed out by CP2K in the MOLog files while I'm
> completely using CP2K data output. I think that the diagonalizer are
> similar and should not be different or at least not a lot but I don't know
> what is missing here.
>
> For example, for the first MO, the numpy diagonalizer gives:
> ```
> [ *0.24013208* 0.22018022 -0.31897544 0.31487772 0.03667346 -0.06520435
> -0.17002725 -0.08236077 0.07229922 -0.0671756 -0.01027799 -0.00122538
> -0.01032485 0.02372487 -0.04522648 0.07152516 -0.02957845 -0.04862388
> 0.21459305 -0.2126356 -0.17272129 -0.87616482 0.55365848 -0.32681116
> -0.14926625 -0.16854633 -0.42447934 0.59950996 0.07111907 -0.2591646 ]
> ```
> while CP2K output is:
> ```
> [ *0.24013208* -0.04335288 -0.03266057 -0.02886998 0.25193464 -0.05879551
> -0.03198254 0.01560468 0.25274078 0.02363462 -0.03533591 -0.04778031
> 0.27746047 -0.02251021 0.03359148 0.0590378 0.25630252 0.0619227 0.01419578
> -0.0243776 0.27224724 0.03675219 0.05132162 0.0233777 0.04862524 0.04652153
> 0.04919569 0.05200084 0.04633218 0.05580193]```
> You can see that the first element of the first eigenvector is the same
> while others are not. I also tried using higher number of digits while
> printing out CP2K output and also `scipy` diagonalizers but all give
> similar results.
>
> For the convergence I compute the commutator relation and when computing
> the norm of the matrix I get a good convergence results in agreement with
> CP2K output:
> e = KPS-SPK
> ```
> e = np.linalg.multi_dot([K,P,S])-np.linalg.multi_dot([S,P,K])
> print(np.linalg.norm(e))
> >>> 1.2473125843097798e-08
> ```
>
> I highly appreciate your time and any suggestion to get the correct
> results.
>
> Thanks in advance.
>
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>

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