Source code for strawberryfields.apps.qchem.utils

# Copyright 2020 Xanadu Quantum Technologies Inc.

# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at


# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
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This module contains various utility functions needed to perform quantum chemistry calculations with
Strawberry Fields.
from typing import Tuple

import numpy as np
from scipy.constants import c, h, m_u, pi

[docs]def duschinsky( Li: np.ndarray, Lf: np.ndarray, ri: np.ndarray, rf: np.ndarray, wf: np.ndarray, m: np.ndarray ) -> Tuple[np.ndarray, np.ndarray]: r"""Generate the Duschinsky rotation matrix :math:`U` and displacement vector :math:`\delta`. The Duschinsky transformation relates the normal coordinates of the initial and final states in a vibronic transition, :math:`q_i` and :math:`q_f` respectively, as: .. math:: q_f = U q_i + d, where :math:`U` is the Duschinsky rotation matrix and :math:`d` is a vector giving the displacement between the equilibrium structures of the two states involved in the vibronic transition. The normal coordinates of a molecule can be represented in terms of atomic displacements as: .. math:: q = L^T \sqrt{m} (r -r_e), where :math:`r_e` represents the equilibrium geometry of the molecule, :math:`m` represents atomic masses and :math:`L` is a matrix containing the eigenvectors of the mass-weighted Hessian. The Duschinsky parameters :math:`U` and :math:`d` can be obtained as: .. math:: U = L_f^T L_i, .. math:: d = L_f^T \sqrt{m} (r_e^i-r_e^f). Note that :math:`i` and :math:`f` refer to the initial and final states, respectively. The parameter :math:`d` is usually represented as a dimensionless parameter :math:`\delta` as: .. math:: \delta = l^{-1} d, where :math:`l` is a diagonal matrix containing the vibrational frequencies :math:`\omega` of the final state: .. math:: l_{kk} = \left ( \frac{\hbar }{2 \pi \omega_k c} \right )^{1/2}, where :math:`\hbar` is the reduced Planck constant and :math:`c` is the speed of light. The vibrational normal mode matrix for a molecule with :math:`M` vibrational modes and :math:`N` atoms is a :math:`3N \times M` matrix where :math:`M = 3N - 6` for nonlinear molecules and :math:`M = 3N - 5` for linear molecules. The Duschinsky rotation matrix of a molecule is an :math:`M \times M` matrix and the Duschinsky displacement vector has :math:`M` components. **Example usage:** >>> Li = np.array([[-0.28933191], [0.0], [0.0], [0.95711104], [0.0], [0.0]]) >>> Lf = np.array([[-0.28933191], [0.0], [0.0], [0.95711104], [0.0], [0.0]]) >>> ri = np.array([-0.0236, 0.0, 0.0, 1.2236, 0.0, 0.0]) >>> rf = np.array([0.0, 0.0, 0.0, 1.4397, 0.0, 0.0]) >>> wf = np.array([1363.2]) >>> m = np.array([11.0093] * 3 + [1.0078] * 3) >>> U, delta = duschinsky(Li, Lf, ri, rf, wf, m) >>> U, delta (array([[0.99977449]]), array([-1.17623073])) Args: Li (array): mass-weighted normal modes of the initial electronic state Lf (array): mass-weighted normal modes of the final electronic state ri (array): equilibrium molecular geometry of the initial electronic state rf (array): equilibrium molecular geometry of the final electronic state wf (array): normal mode frequencies of the final electronic state in units of :math:`\mbox{cm}^{-1}` m (array): atomic masses in unified atomic mass units Returns: tuple[array, array]: Duschinsky rotation matrix :math:`U`, Duschinsky displacement vector :math:`\delta` """ U = Lf.T @ Li d = Lf.T * m ** 0.5 @ (ri - rf) l0_inv = np.diag((h / (wf * 100.0 * c)) ** (-0.5) * 2.0 * pi) / 1.0e10 * m_u ** 0.5 delta = np.array(d @ l0_inv) return U, delta
[docs]def read_gamess(file) -> Tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray]: r"""Reads molecular data from the output file generated by the GAMESS quantum chemistry package :cite:`schmidt1993general`. This function extracts the atomic coordinates (r), atomic masses (m), vibrational frequencies (w), and normal modes (l) of a molecule from the output file of a vibrational frequency calculation performed with the GAMESS quantum chemistry package. The output file must contain the results of a `RUNTYP=HESSIAN` calculation performed with GAMESS. We recommend checking the output of this function with the GAMESS results to assure that the GAMESS output file is parsed correctly. **Example usage:** >>> r, m, w, l = read_gamess('../BH_data.out') >>> r # atomic coordinates array([[0.0000000, 0.0000000, 0.0000000], [1.2536039, 0.0000000, 0.0000000]]) >>> m # atomic masses array([11.00931, 1.00782]) >>> w # vibrational frequencies array([19.74, 19.73, 0.00, 0.00, 0.00, 2320.32]) >>> l # normal modes array([[-0.0000000e+00, -7.5322000e-04, -8.7276210e-02, 0.0000000e+00, 8.2280900e-03, 9.5339055e-01], [-0.0000000e+00, -8.7276210e-02, 7.5322000e-04, 0.0000000e+00, 9.5339055e-01, -8.2280900e-03], [ 2.8846925e-01, -2.0000000e-08, 2.0000000e-08, 2.8846925e-01, -2.0000000e-08, 2.0000000e-08], [ 2.0000000e-08, 2.8846925e-01, -2.0000000e-08, 2.0000000e-08, 2.8846925e-01, -2.0000000e-08], [-2.0000000e-08, 2.0000000e-08, 2.8846925e-01, -2.0000000e-08, 2.0000000e-08, 2.8846925e-01], [-8.7279460e-02, 0.0000000e+00, 0.0000000e+00, 9.5342606e-01, -0.0000000e+00, -0.0000000e+00]]) Args: file (str): path to the GAMESS output file Returns: tuple[array, array, array, array]: atomic coordinates, atomic masses, normal mode frequencies, normal modes """ with open(file, "r") as f: r = [] m = [] w = [] l = [] for line in f: if "INPUT CARD> $data" in line or "INPUT CARD> $DATA" in line: line = [next(f) for _ in range(3)][-1] while "end" not in line and "END" not in line: r.append(np.array(line.rstrip().split()[-3:], float)) line = next(f).rstrip() if "ATOMIC WEIGHTS" in line: next(f) for _ in range(len(r)): m.append(np.array(next(f).rstrip().split()[-1:], float)) if "FREQUENCY" in line: line = line.rstrip().split() n_mode = len(line) - 1 w.append(np.array(line[-n_mode:], float)) while f.readline() != "\n": pass d = [] for _ in range(len(r) * 3): d.append(f.readline().rstrip().split()[-n_mode:]) l.append(np.array(d, float).T) if not r: raise ValueError("No atomic coordinates found in the output file") if not m: raise ValueError("No atomic masses found in the output file") if not w: raise ValueError("No vibrational frequencies found in the output file") return ( np.concatenate(r).reshape(len(r), 3), np.concatenate(m), np.concatenate(w), np.concatenate(l), )