We cannot copy.deepcopy Topology object
This is currently done [in `NullProposalEngine.propose`](https://github.com/choderalab/perses/blob/benchmark/perses/rjmc/topology_proposal.py#L1682) and in [`PolymerProposalEngine.propose`](https://github.com/choderalab/perses/blob/benchmark/perses/rjmc/topology_proposal.py#L232-L236). See https://github.com/choderalab/perses/pull/281 for a detailed explanation of why we cannot do this and what the fix is.

Using `deepcopy` on `Topology` objects causes Perses to fail with `openmm 7.1.0` builds.

`perses` will not run correctly on `openmm 7.0.1` because of known bugs in `CustomIntegrator`. We *must* use `7.1.0`.
diff --git a/perses/rjmc/topology_proposal.py b/perses/rjmc/topology_proposal.py
index 894bc00c..543ac32b 100644
--- a/perses/rjmc/topology_proposal.py
+++ b/perses/rjmc/topology_proposal.py
@@ -230,10 +230,12 @@ class PolymerProposalEngine(ProposalEngine):
             mapping
         """
         # old_topology : simtk.openmm.app.Topology
-        old_topology = copy.deepcopy(current_topology)
+        old_topology = app.Topology()
+        self._append_topology(old_topology, current_topology)
 
         # new_topology : simtk.openmm.app.Topology
-        new_topology = copy.deepcopy(current_topology)
+        new_topology = app.Topology()
+        self._append_topology(new_topology, current_topology)
 
         # Check that old_topology and old_system have same number of atoms.
         old_system = current_system
@@ -1679,7 +1681,8 @@ class NullProposalEngine(SmallMoleculeSetProposalEngine):
         old_key = current_topology._state_key
         new_key = [key for key in self._fake_states if key != old_key][0]
 
-        new_topology = copy.deepcopy(current_topology)
+        new_topology = app.Topology()
+        self._append_topology(new_topology, current_topology)
         new_topology._state_key = new_key
         new_system = copy.deepcopy(current_system)
         atom_map = self._make_skewed_atom_map(current_topology)
diff --git a/perses/tests/benchmark.py b/perses/tests/benchmark.py
deleted file mode 100644
index 552fc7a4..00000000
--- a/perses/tests/benchmark.py
+++ /dev/null
@@ -1,184 +0,0 @@
-from simtk import openmm, unit
-from simtk.openmm import app
-import os, os.path
-import sys, math
-from unittest import skipIf
-import numpy as np
-from functools import partial
-from pkg_resources import resource_filename
-from openeye import oechem
-if sys.version_info >= (3, 0):
-    from io import StringIO
-    from subprocess import getstatusoutput
-else:
-    from cStringIO import StringIO
-    from commands import getstatusoutput
-import matplotlib as mpl
-mpl.use('Agg')
-import seaborn as sns
-
-import matplotlib.pyplot as plt
-
-################################################################################
-# NUMBER OF ATTEMPTS
-################################################################################
-niterations = 50
-ENV = 'vacuum'
-################################################################################
-# CONSTANTS
-################################################################################
-
-kB = unit.BOLTZMANN_CONSTANT_kB * unit.AVOGADRO_CONSTANT_NA
-temperature = 300.0 * unit.kelvin
-kT = kB * temperature
-beta = 1.0/kT
-
-functions_hybrid = {
-    'lambda_sterics' : 'lambda',
-    'lambda_electrostatics' : 'lambda',
-    'lambda_bonds' : 'lambda',#'1.0',
-    'lambda_angles' : 'lambda',#'0.1*lambda+0.9',
-    'lambda_torsions' : 'lambda',#'0.7*lambda+0.3'
-}
-functions_twostage = {
-    'lambda_sterics' : '(2*lambda)^4 * step(0.5 - lambda) + (1.0 - step(0.5 - lambda))',
-    'lambda_electrostatics' : '2*(lambda - 0.5) * step(lambda - 0.5)',
-    'lambda_bonds' : '1.0', # don't soften bonds
-    'lambda_angles' : '0.1*lambda+0.9',
-    'lambda_torsions' : '0.7*lambda+0.3'
-}
-
-def plot_logPs(logps, molecule_name, scheme, component):
-    """
-    Create line plot of mean and standard deviation of given logPs.
-
-    Arguments:
-    ----------
-        logps: dict { int : np.ndarray }
-            key : number of total NCMC steps
-            value : array of `niterations` logP values
-        molecule_name : str
-            The molecule featured in the NullTestSystem being analyzed
-            in ['naphthalene','butane','propane']
-        scheme : str
-            Which NCMC scheme is being used
-            in ['hybrid','two-stage']
-        component : str
-            Which logP is being plotted
-            in ['NCMC','EXEN']
-    """
-    x = logps.keys()
-    x.sort()
-    y = [logps[steps].mean() for steps in x]
-    dy = [logps[steps].std() for steps in x]
-    plt.fill_between(x, [mean - dev for mean, dev in zip(y, dy)], [mean + dev for mean, dev in zip(y, dy)])
-    plt.plot(x, y, 'k')
-    plt.xscale('log')
-
-    plt.title("Log acceptance probability of {0} ExpandedEnsemble for {1}".format(scheme, molecule_name))
-    plt.ylabel('logP')
-    plt.xlabel('ncmc steps')
-    plt.savefig('{0}_{1}_{2}{3}_logP'.format(ENV, molecule_name, scheme, component))
-    print('Saved plot to {0}_{1}_{2}{3}_logP.png'.format(ENV, molecule_name, scheme, component))
-    plt.clf()
-
-def benchmark_exen_ncmc_protocol(analyses, molecule_name, scheme):
-    """
-    For each combination of system and scheme, results are analyzed for
-    the following:
-    * Over the whole range of total steps:
-        * Plot mean and standard deviation of NCMC logP as a function of
-          total steps
-        * Plot mean and standard deviation of EXEN logP as a function of
-          total steps
-
-    Arguments:
-    ----------
-        analyses : dict { int : perses.Analysis }
-            key : number of total NCMC steps
-            value : analysis object contained stored information
-        molecule_name : str
-            The molecule featured in the NullTestSystem being analyzed
-            in ['naphthalene','butane','propane']
-        scheme : str
-            Which NCMC scheme is being used
-            in ['hybrid','two-stage']
-
-    Creates 2 plots every time it is called
-    """
-    components = {
-        'logp_accept' : 'EXEN',
-        'logp_ncmc' : 'NCMC',
-    }
-
-    for component in components.keys():
-        print('Finding {0} over nsteps for {1} with {2} NCMC'.format(component, molecule_name, scheme))
-        logps = dict()
-        for nsteps, analysis in analyses.items():
-            ee_sam = analysis._ncfile.groups['ExpandedEnsembleSampler']
-            niterations = ee_sam.variables[component].shape[0]
-            logps[nsteps] = np.zeros(niterations, np.float64)
-            for n in range(niterations):
-                logps[nsteps][n] = ee_sam.variables[component][n]
-        plot_logPs(logps, molecule_name, scheme, components[component])
-
-def benchmark_ncmc_work_during_protocol():
-    """
-    Run 50 iterations of ExpandedEnsembleSampler for NullTestSystems
-    over a range of total NCMC steps [0, 1, 10, 100, 1000, 10000].
-
-    Benchmark is repeated for Naphthalene, Butane, and Propane test
-    systems, using two-stage and hybrid NCMC.
-
-    For each combination of system and scheme, results are analyzed for
-    the following:
-    * For a given total number of steps:
-        * For NCMC steps 100 and above, plot work done by ncmc integrator
-          over the course of the protocol
-        * Plot histograms of the contributions of each component to the
-          overall log acceptance probability
-    * Over the whole range of total steps:
-        * Plot mean and standard deviation of NCMC logP as a function of
-          total steps
-        * Plot mean and standard deviation of EXEN logP as a function of
-          total steps
-    """
-    from perses.tests.testsystems import NaphthaleneTestSystem, ButaneTestSystem, PropaneTestSystem
-    from perses.analysis import Analysis
-    import netCDF4 as netcdf
-    import pickle
-    import codecs
-    molecule_names = {
-        'naphthalene' : NaphthaleneTestSystem,
-        'butane' : ButaneTestSystem,
-        'propane' : PropaneTestSystem,
-    }
-    methods = {
-        'hybrid' : ['geometry-ncmc-geometry', functions_hybrid],
-        'two-stage' : ['ncmc-geometry-ncmc', functions_twostage],
-    }
-
-    for molecule_name, NullProposal in molecule_names.items():
-        print('\\nNow testing {0} null transformations'.format(molecule_name))
-        for name, [scheme, functions] in methods.items():
-            analyses = dict()
-            for ncmc_nsteps in [0, 1, 10, 100, 1000, 10000]:
-                print('Running {0} {2} ExpandedEnsemble steps for {1} iterations'.format(ncmc_nsteps, niterations, name))
-                testsystem = NullProposal(storage_filename='{0}_{1}-{2}steps.nc'.format(molecule_name, name, ncmc_nsteps), scheme=scheme, options={'functions' : functions, 'nsteps' : ncmc_nsteps})
-                testsystem.exen_samplers[ENV].verbose = False
-                testsystem.exen_samplers[ENV].sampler.verbose = False
-                if name == 'hybrid':
-                    testsystem.exen_samplers[ENV].ncmc_engine.softening = 1.0
-                testsystem.exen_samplers[ENV].run(niterations=niterations)
-
-                analysis = Analysis(testsystem.storage_filename)
-                print(analysis.get_environments())
-                if ncmc_nsteps > 99:
-                    analysis.plot_ncmc_work('{0}_{1}-ncmc_work_over_{2}_steps.pdf'.format(molecule_name, name, ncmc_nsteps))
-                analysis.plot_exen_logp_components()
-                analyses[ncmc_nsteps] = analysis
-            benchmark_exen_ncmc_protocol(analyses, molecule_name, name)
-
-
-if __name__ == "__main__":
-    benchmark_ncmc_work_during_protocol()
['perses/tests/benchmark.py', 'perses/rjmc/topology_proposal.py']