#!/usr/bin/env python
# Copyright 2014-2022 The PySCF Developers. All Rights Reserved.
#
# 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
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# Authors: Matthew Hennefarth <matthew.hennefarth@gmail.com>,
# Aniruddha Seal <aniruddhaseal2011@gmail.com>
import os
import numpy as np
from pyscf import data
from pyscf import lib
from pyscf.lib import logger
from pyscf.grad.rhf import GradientsBase
[docs]
class Frame:
'''Basic class to hold information at each time step of a MD simulation
Attributes:
ekin : float
Kinetic energy
epot : float
Potential energy (electronic energy)
etot : float
Total energy, sum of the potential and kinetic energy
coord : 2D array with shape (natm, 3)
Geometry of the system at the current time step
veloc : 2D array with shape (natm, 3)
Velocities of the system at the current time step
time : float
Time for which this frame represents
'''
def __init__(self,
ekin=None,
epot=None,
coord=None,
veloc=None,
time=None):
self.ekin = ekin
self.epot = epot
self.etot = self.ekin + self.epot
self.coord = coord
self.veloc = veloc
self.time = time
def _toframe(integrator):
'''Convert an _Integrator to a Frame given current saved data.
Args:
integrator : md.integrator._Integrator object
Returns:
Frame with all data taken from the integrator.
'''
return Frame(ekin=integrator.ekin,
epot=integrator.epot,
coord=integrator.mol.atom_coords(),
veloc=integrator.veloc,
time=integrator.time)
def _write(dev, mol, vec, atmlst=None):
'''Format output of molecular vector quantity.
Args:
dev : lib.logger.Logger object
mol : gto.mol object
vec : 2D array with shape (mol.natm, 3)
atmlst : array of indices to pull atoms from.
Must be smaller than mol.natm.
'''
if atmlst is None:
atmlst = range(mol.natm)
dev.stdout.write(' x y z\n')
for k, ia in enumerate(atmlst):
dev.stdout.write(
'%d %s %15.10f %15.10f %15.10f\n' %
(ia, mol.atom_symbol(ia), vec[k, 0], vec[k, 1], vec[k, 2]))
[docs]
def kernel(integrator, verbose=logger.NOTE):
log = logger.new_logger(integrator, verbose)
t0 = (logger.process_clock(), logger.perf_counter())
log.debug('Start BOMD')
integrator.mol = integrator.mol.copy()
# Begin the iterations to run molecular dynamics
t1 = t0
for iteration, frame in enumerate(integrator):
log.note('----------- %s final geometry -----------',
integrator.__class__.__name__)
_write(integrator, integrator.mol, frame.coord)
log.note('----------------------------------------------')
log.note('------------ %s final velocity -----------',
integrator.__class__.__name__)
_write(integrator, integrator.mol, frame.veloc)
log.note('----------------------------------------------')
log.note('Ekin = %17.13f', frame.ekin)
log.note('Epot = %17.13f', frame.epot)
log.note('Etot = %17.13f', frame.etot)
t1 = log.timer('BOMD iteration %d' % iteration, *t1)
t0 = log.timer('BOMD', *t0)
return integrator
class _Integrator(lib.StreamObject):
'''Integrator abstract base class. Should never be directly constructed,
but inherited from.
Args:
method : lib.GradScanner, rhf.GradientsBase instance, or
has nuc_grad_method method.
Method by which to compute the energy gradients and energies
in order to propagate the equations of motion. Realistically,
it can be any callable object such that it returns the energy
and potential energy gradient when given a mol.
Attributes:
incore_anyway : bool
If true, then it will save every frame in memory.
False, no frames are saved.
veloc : ndarray
Initial velocity for the simulation. Values should be given
in atomic units (Bohr/a.u.). Dimensions should be (natm, 3) such as
[[x1, y1, z1],
[x2, y2, z2],
[x3, y3, z3]]
verbose : int
Print level
steps : int
Number of steps to take when the kernel or run function is called.
dt : float
Time between steps. Given in atomic units.
stdout : file object
Default is self.scanner.mol.stdout.
data_output : file object
Stream to write energy and temperature to
during the course of the simulation.
trajectory_output : file object
Stream to write the trajectory to during the course of the
simulation. Written in xyz format.
frames : ndarray of Frames or None
If incore_anyway is true, then this will hold a list of frames
corresponding to the simulation trajectory.
epot : float
Potential energy of the last time step during the simulation.
ekin : float
Kinetic energy of the last time step during the simulation
time : float
Time of the last step during the simulation.
callback : function(envs_dict) => None
Callback function takes one dict as the argument which is
generated by the builtin function :func:`locals`, so that the
callback function can access all local variables in the current
environment.
'''
def __init__(self, method, **kwargs):
if isinstance(method, lib.GradScanner):
self.scanner = method
elif isinstance(method, GradientsBase):
self.scanner = method.as_scanner()
elif getattr(method, 'nuc_grad_method', None):
self.scanner = method.nuc_grad_method().as_scanner()
else:
raise NotImplementedError('Nuclear gradients of %s not available' %
method)
self.mol = self.scanner.mol
self.stdout = self.mol.stdout
self.incore_anyway = self.mol.incore_anyway
self.veloc = None
self.verbose = self.mol.verbose
self.steps = 1
self.dt = 10
self.frames = None
self.epot = None
self.ekin = None
self.time = 0
self.data_output = None
self.trajectory_output = None
self.callback = None
# Cache the masses into a list, they will be in atomic units
self._masses = None
self.__dict__.update(kwargs)
def kernel(self, veloc=None, steps=None, dump_flags=True, verbose=None):
'''Runs the molecular dynamics simulation.
Args:
veloc : ndarray
Initial velocity for the simulation. Values should be given
in atomic units (Bohr/a.u.). Dimensions should be (natm, 3)
such as
[[x1, y1, z1],
[x2, y2, z2],
[x3, y3, z3]]
steps : int
Number of steps to take when the kernel or run function
is called.
dump_flags : bool
Print flags to output.
verbose : int
Print level
Returns:
_Integrator with final epot, ekin, temp,
mol, and veloc of the simulation.
'''
if veloc is not None:
self.veloc = veloc
if steps is not None:
self.steps = steps
if verbose is None:
verbose = self.verbose
# Default velocities are 0 if none specified
if self.veloc is None:
self.veloc = np.full((self.mol.natm, 3), 0.0)
# Store the masses into a cached variable,
# so we don't have to keep looking them up
self._masses = np.array([
data.elements.COMMON_ISOTOPE_MASSES[m] * data.nist.AMU2AU
for m in self.mol.atom_charges()])
# avoid opening data_output file twice
if type(self.data_output) is str:
if self.verbose > logger.QUIET:
if os.path.isfile(self.data_output):
print('overwrite data output file: %s' %
self.data_output)
else:
print('data output file: %s' % self.data_output)
if self.data_output == '/dev/null':
self.data_output = open(os.devnull, 'w')
else:
self.data_output = open(self.data_output, 'w')
self.data_output.write(
'time Epot Ekin '
'Etot T\n'
)
# avoid opening trajectory_output file twice
if type(self.trajectory_output) is str:
if self.verbose > logger.QUIET:
if os.path.isfile(self.trajectory_output):
print('overwrite energy output file: %s' %
self.trajectory_output)
else:
print('trajectory output file: %s' %
self.trajectory_output)
if self.trajectory_output == '/dev/null':
self.trajectory_output = open(os.devnull, 'w')
else:
self.trajectory_output = open(self.trajectory_output, 'w')
log = logger.new_logger(self, verbose)
self.check_sanity()
if dump_flags and self.verbose > logger.NOTE:
self.dump_input()
return kernel(self, verbose=log)
def dump_input(self, verbose=None):
log = logger.new_logger(self, verbose)
log.info('')
log.info('******** BOMD flags ********')
log.info('dt = %f', self.dt)
log.info('Iterations = %d', self.steps)
log.info(' Initial Velocity ')
log.info(' vx vy vz')
for i, (e, v) in enumerate(zip(self.mol.elements, self.veloc)):
log.info('%d %s %.8E %.8E %.8E', i, e, *v)
def check_sanity(self):
assert self.time >= 0
assert self.dt > 0
assert self.steps > 0
assert self.veloc is not None
assert self.veloc.shape == (self.mol.natm, 3)
assert self.scanner is not None
return self
def compute_kinetic_energy(self):
'''Compute the kinetic energy of the current frame.'''
# TODO, can make this cleaner by removing an explicit zip and
# try to leverage numpy vectors
energy = 0
for v, m in zip(self.veloc, self._masses):
energy += 0.5 * m * np.linalg.norm(v) ** 2
return energy
def temperature(self):
'''Returns the temperature of the system'''
# checked against ORCA for linear and non-linear molecules
dof = 3 * len(self.mol.atom_coords())
# Temp = 2/(3*k*N_f) * KE
# = 2/(3*k*N_f)*\sum_i (1/2 m_i v_i^2)
return ((2 * self.ekin) / (
dof * data.nist.BOLTZMANN / data.nist.HARTREE2J))
def __iter__(self):
self._step = 0
self._log = logger.new_logger(self, self.verbose)
return self
def __next__(self):
if self._step < self.steps:
if self._log.verbose >= lib.logger.NOTE:
self._log.note('\nBOMD Time %.2f', self.time)
current_frame = self._next()
if self.incore_anyway:
self.frames.append(current_frame)
if self.data_output is not None:
self._write_data()
if self.trajectory_output is not None:
self._write_coord()
if callable(self.callback):
mol = self.mol
scanner = self.scanner
self.callback(locals())
self._step += 1
self.time += self.dt
return current_frame
else:
raise StopIteration
def _next(self):
'''Determines the next step in the molecular dynamics simulation.
Integrates to the next time step. Must be implemented in derived
classes.
Returns: 'Frame' which contains the new geometry, velocity,
time step, and energy.
'''
raise NotImplementedError('Method Not Implemented')
def _write_data(self):
'''Writes out the potential, kinetic, and total energy, temperature to the
self.data_output stream. '''
output = '%8.2f %.12E %.12E %.12E %3.4f' % (self.time,
self.epot,
self.ekin,
self.ekin + self.epot,
self.temperature())
# We follow OM of writing all the states at the end of the line
if getattr(self.scanner.base, 'e_states', None) is not None:
if len(self.scanner.base.e_states) > 1:
for e in self.scanner.base.e_states:
output += ' %.12E' % e
self.data_output.write(output + '\n')
# If we don't flush, there is a possibility of losing data
self.data_output.flush()
def _write_coord(self):
'''Writes out the current geometry to the self.trajectory_output
stream in xyz format. '''
self.trajectory_output.write('%s\nMD Time %.2f\n' %
(self.mol.natm, self.time))
self.trajectory_output.write(self.mol.tostring(format='raw') + '\n')
# If we don't flush, there is a possibility of losing data
self.trajectory_output.flush()
[docs]
class VelocityVerlet(_Integrator):
'''Velocity Verlet algorithm
Args:
method : lib.GradScanner or rhf.GradientsBase instance, or
has nuc_grad_method method.
Method by which to compute the energy gradients and energies
in order to propagate the equations of motion. Realistically,
it can be any callable object such that it returns the energy
and potential energy gradient when given a mol.
Attributes:
accel : ndarray
Current acceleration for the simulation. Values are given
in atomic units (Bohr/a.u.^2). Dimensions is (natm, 3) such as
[[x1, y1, z1],
[x2, y2, z2],
[x3, y3, z3]]
'''
def __init__(self, method, **kwargs):
super().__init__(method, **kwargs)
self.accel = None
def _next(self):
'''Computes the next frame of the simulation and sets all internal
variables to this new frame. First computes the new geometry,
then the next acceleration, and finally the velocity, all according
to the Velocity Verlet algorithm.
Returns:
The next frame of the simulation.
'''
# If no acceleration, compute that first, and then go
# onto the next step
if self.accel is None:
next_epot, next_accel = self._compute_accel()
else:
self.mol.set_geom_(self._next_geometry(), unit='B')
self.mol.build()
next_epot, next_accel = self._compute_accel()
self.veloc = self._next_velocity(next_accel)
self.epot = next_epot
self.ekin = self.compute_kinetic_energy()
self.accel = next_accel
return _toframe(self)
def _compute_accel(self):
'''Given the current geometry, computes the acceleration
for each atom.'''
e_tot, grad = self.scanner(self.mol)
if not self.scanner.converged:
raise RuntimeError('Gradients did not converge!')
a = -1 * grad / self._masses.reshape(-1, 1)
return e_tot, a
def _next_geometry(self):
'''Computes the next geometry using the Velocity Verlet algorithm. The
necessary equations of motion for the position is
r(t_i+1) = r(t_i) + /delta t * v(t_i) + 0.5(/delta t)^2 a(t_i)
'''
return self.mol.atom_coords() + self.dt * self.veloc + \
0.5 * (self.dt ** 2) * self.accel
def _next_velocity(self, next_accel):
'''Compute the next velocity using the Velocity Verlet algorithm. The
necessary equations of motion for the velocity is
v(t_i+1) = v(t_i) + 0.5(a(t_i+1) + a(t_i))'''
return self.veloc + 0.5 * self.dt * (self.accel + next_accel)
[docs]
class NVTBerendson(_Integrator):
'''Berendsen (constant N, V, T) molecular dynamics
Args:
method : lib.GradScanner or rhf.GradientsMixin instance, or
has nuc_grad_method method.
Method by which to compute the energy gradients and energies
in order to propagate the equations of motion. Realistically,
it can be any callable object such that it returns the energy
and potential energy gradient when given a mol.
T : float
Target temperature for the NVT Ensemble. Given in K.
taut : float
Time constant for Berendsen temperature coupling.
Given in atomic units.
Attributes:
accel : ndarray
Current acceleration for the simulation. Values are given
in atomic units (Bohr/a.u.^2). Dimensions is (natm, 3) such as
[[x1, y1, z1],
[x2, y2, z2],
[x3, y3, z3]]
'''
def __init__(self, method, T, taut, **kwargs):
self.T = T
self.taut = taut
self.accel = None
super().__init__(method, **kwargs)
def _next(self):
'''Computes the next frame of the simulation and sets all internal
variables to this new frame. First computes the new geometry,
then the next acceleration, and finally the velocity, all according
to the Velocity Verlet algorithm.
Returns:
The next frame of the simulation.
'''
# If no acceleration, compute that first, and then go
# onto the next step
if self.accel is None:
next_epot, next_accel = self._compute_accel()
else:
self._scale_velocities()
self.mol.set_geom_(self._next_geometry(), unit='B')
self.mol.build()
next_epot, next_accel = self._compute_accel()
self.veloc = self._next_velocity(next_accel)
self.epot = next_epot
self.ekin = self.compute_kinetic_energy()
self.accel = next_accel
return _toframe(self)
def _compute_accel(self):
'''Given the current geometry, computes the acceleration
for each atom.'''
e_tot, grad = self.scanner(self.mol)
if not self.scanner.converged:
raise RuntimeError('Gradients did not converge!')
a = -1 * grad / self._masses.reshape(-1, 1)
return e_tot, a
def _scale_velocities(self):
'''NVT Berendsen velocity scaling
v_rescale(t) = v(t) * (1 + ((T_target/T - 1)
* (/delta t / taut)))^(0.5)
'''
tautscl = self.dt / self.taut
scl_temp = np.sqrt(1.0 + (self.T / self.temperature() - 1.0) * tautscl)
# Limit the velocity scaling to reasonable values
# (taken from ase md/nvtberendson.py)
if scl_temp > 1.1:
scl_temp = 1.1
if scl_temp < 0.9:
scl_temp = 0.9
self.veloc = self.veloc * scl_temp
return
def _next_geometry(self):
'''Computes the next geometry using the Velocity Verlet algorithm. The
necessary equations of motion for the position is
r(t_i+1) = r(t_i) + /delta t * v(t_i) + 0.5(/delta t)^2 a(t_i)
'''
return self.mol.atom_coords() + self.dt * self.veloc + \
0.5 * (self.dt ** 2) * self.accel
def _next_velocity(self, next_accel):
'''Compute the next velocity using the Velocity Verlet algorithm. The
necessary equations of motion for the velocity is
v(t_i+1) = v(t_i) + /delta t * 0.5(a(t_i+1) + a(t_i))'''
return self.veloc + 0.5 * self.dt * (self.accel + next_accel)
