12/5/2023 0 Comments Test and zmatrix together![]() If we define the dihedral angle 2-1-5-8 (fig.1) to be scanned from 180.0 deg to 0.0 by 45.0 degrees increments then the second step of the scan would look distorted like the molecule on figure 2. Lets say we want to calculate the energy barrier associated with the rotation of a dihedral angle on ethane. Therefore the use of wildcards is compulsory and it is illustrated below. ![]() The worst case scenario would consist of the molecule’s complete distortion from any physically achievable structure, making the calculation end with an error or by providing meaningless results. This means that functional groups can be destroyed on each step and in the best case scenario the optimization algorithm will put it back together again at, of course, some unnecessary computational cost. A common mistake is to define the variable to scan without taking into consideration all the other variables which depend from the first. Using internal coordinates becomes compulsory and a well-defined Z-Matrix is preferable. vander(,8) produces an array of powers of 4, which in the (matrix multiplication) gets dot-producted with each binary vector, producing a similar s (transposed differently), and the rest is similar.The use of Internal Redundant coordinates (through the Opt=ModRedundant option) must not be overlooked! This option performes a geometry optimization at each step while maintaining the scanned variable constant, which is referred to as a Relaxed Potential Energy Surface (PES) Scan. It is passed to mat ("Interpret the input as a matrix"), which in particular makes it 2-dimensional, while also changing its type to uint8, which is necessary for the next function unpackbits, which breaks the numbers down into their binary representations, across the added dimension. c_ makes a vertical version of that sequence, which is doubled and added to the original sequence, which (by broadcasting) produces a table of sums, which is the required result. The matrix product ( is equivalent to taking the dot product of each broken-down number with b this squares each nonzero bit, changing powers of 2 into powers of 4, and adds them back up, producing a horizontal sequence 0, 1, 4, 5, 16, 17, 20, 21. The bitwise AND, with broadcasting, produces a table of values, splitting the numbers into their constituent bits. r_ produces 0 (inc.) to n (exc.), horizontally, and the left shift makes the corresponding powers of 2, saved in b. Python 3 with numpy, 91 87 74 70 69 67 bytes lambda numpy import*Ĭ_ produces an array of the numbers 0 (inclusive) to 2 n (exclusive), vertically. " - zip (rows of M) with (rows of that) and apply: number of times: chain's left argument -> n Ġ - group indices (of implicit ) by value -> ] (our initial M) Ġ "FL+ƊZƊ⁸¡⁺ - Link: non-negative integer, n ![]() Starts with ] and repeatedly applies a function that creates the required new entries to the right (and then below, via the transposed matrix) by adding the number of current elements to each element. Try it online! (Footer formats as a Python list for clarity.) How? 1 thanks to caird coinheringaahing (we can use 1-based values) Ġ "FL+ƊZƊ⁸¡⁺Ī monadic Link that accepts a non-negative integer and yields the matrix (using the 1-based values option). (Still no clue for the 6 byte code though!) Ḅ4 - convert from base four -> first 2^n terms of the Moser–De Bruijn sequence Ṗ - Cartesian power (n) -> binary representations of Makes a table under \$x+2y\$ where both \$x\$ and \$y\$ are a prefix of the Moser–De Bruijn sequence. (This should work on v7 or later from what I can tell, but in the testing setup I'm using (similar to here), it gives 'instruction not supported' errors on versions lower than v8.4, which doesn't seem right.) Divide the matrix into four quadrants of size \$2^, ! Place the result into memory, advancing the pointer.Given a non-negative integer \$n\$, create a 2D array of size \$2^n × 2^n\$ which is generated in the following manner: Originally from a CMC I proposed for the last BMG event Challenge
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