diff --git a/smee/potentials/nonbonded.py b/smee/potentials/nonbonded.py
index ced5646..d71aee5 100644
--- a/smee/potentials/nonbonded.py
+++ b/smee/potentials/nonbonded.py
@@ -352,10 +352,9 @@ def _integrate_lj_switch(
     )
     coeff_11 = smee.utils.tensor_like([84, -3780, 7560, 2520, -3780, 756], rs) * coeff_0
 
-    r_pow = torch.pow(
-        r, smee.utils.tensor_like([-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2], rs)
-    )
-    r_pow[-3] = torch.log(r)
+    powers = smee.utils.tensor_like([-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2], rs)
+    r_pow = torch.pow(r, powers)
+    r_pow = torch.where(powers == 0, torch.log(r), r_pow)
 
     integral = (
         -(b**3)
diff --git a/smee/tests/convertors/openff/test_nonbonded.py b/smee/tests/convertors/openff/test_nonbonded.py
index 2a00bbe..5220546 100644
--- a/smee/tests/convertors/openff/test_nonbonded.py
+++ b/smee/tests/convertors/openff/test_nonbonded.py
@@ -1,11 +1,10 @@
 import importlib.util
 
-import pytest
-
 import openff.interchange
 import openff.interchange.models
 import openff.toolkit
 import openff.units
+import pytest
 import torch
 
 import smee
diff --git a/smee/tests/convertors/openff/test_openff.py b/smee/tests/convertors/openff/test_openff.py
index 955e08f..53c29be 100644
--- a/smee/tests/convertors/openff/test_openff.py
+++ b/smee/tests/convertors/openff/test_openff.py
@@ -2,10 +2,10 @@
 
 import openff.interchange.models
 import openff.toolkit
-from openff.toolkit.utils.toolkit_registry import toolkit_registry_manager
 import openff.units
 import pytest
 import torch
+from openff.toolkit.utils.toolkit_registry import toolkit_registry_manager
 
 import smee
 import smee.tests.utils
diff --git a/smee/tests/potentials/test_nonbonded.py b/smee/tests/potentials/test_nonbonded.py
index a09d6a5..b73872e 100644
--- a/smee/tests/potentials/test_nonbonded.py
+++ b/smee/tests/potentials/test_nonbonded.py
@@ -16,8 +16,8 @@
     _COULOMB_PRE_FACTOR,
     _compute_dexp_lrc,
     _compute_lj_lrc,
-    _compute_pme_exclusions,
     _compute_pairwise_periodic,
+    _compute_pme_exclusions,
     compute_coulomb_energy,
     compute_dexp_energy,
     compute_lj_energy,
diff --git a/smee/tests/potentials/test_potentials.py b/smee/tests/potentials/test_potentials.py
index 31a6f0e..08c4af0 100644
--- a/smee/tests/potentials/test_potentials.py
+++ b/smee/tests/potentials/test_potentials.py
@@ -232,3 +232,32 @@ def test_compute_energy_v_sites():
     energy_smee = compute_energy(tensor_top, tensor_ff, conformer)
 
     assert torch.isclose(energy_smee, energy_openmm.to(energy_smee.dtype))
+
+
+@pytest.mark.parametrize("periodic", [True, False])
+def test_energy_backward_pass(periodic):
+    tensor_sys, tensor_ff = smee.tests.utils.system_from_smiles(["CCC", "O"], [2, 3])
+    tensor_sys.is_periodic = periodic
+
+    coords, _ = smee.mm.generate_system_coords(tensor_sys, None)
+    coords = torch.tensor(coords.value_in_unit(openmm.unit.angstrom))
+    box_vectors = torch.eye(3, dtype=coords.dtype) * 30.0 if periodic else None
+    coords.requires_grad = True
+
+    for potential in tensor_ff.potentials:
+        potential.parameters.requires_grad = True
+        if potential.attributes is not None:
+            potential.attributes.requires_grad = True
+
+    energy = smee.compute_energy(tensor_sys, tensor_ff, coords, box_vectors)
+    energy.backward()
+
+    assert coords.grad is not None
+    for potential in tensor_ff.potentials:
+        assert potential.parameters.grad is not None
+        assert potential.parameters.grad.shape == potential.parameters.shape
+        assert not torch.isnan(potential.parameters.grad).any()
+        if potential.attributes is not None:
+            assert potential.attributes.grad is not None
+            assert potential.attributes.grad.shape == potential.attributes.shape
+            assert not torch.isnan(potential.attributes.grad).any()