dorsal/arxiv
View SchemaExplicit factorization of external coordinates in constrained Statistical Mechanics models
| Authors | Pablo Echenique, Ivan Calvo |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0512033 |
| URL | https://arxiv.org/abs/q-bio/0512033 |
| DOI | 10.1002/jcc.20499 |
| Journal | J. Comp. Chem. 27 (2006) 1748-1755 |
Abstract
If a macromolecule is described by curvilinear coordinates or rigid constraints are imposed, the equilibrium probability density that must be sampled in Monte Carlo simulations includes the determinants of different mass-metric tensors. In this work, we explicitly write the determinant of the mass-metric tensor G and of the reduced mass-metric tensor g, for any molecule, general internal coordinates and arbitrary constraints, as a product of two functions; one depending only on the external coordinates that describe the overall translation and rotation of the system, and the other only on the internal coordinates. This work extends previous results in the literature, proving with full generality that one may integrate out the external coordinates and perform Monte Carlo simulations in the internal conformational space of macromolecules. In addition, we give a general mathematical argument showing that the factorization is a consequence of the symmetries of the metric tensors involved. Finally, the determinant of the mass-metric tensor G is computed explicitly in a set of curvilinear coordinates specially well-suited for general branched molecules.
{
"annotation_id": "7e3d9200-ab4e-4694-9be9-66447177c924",
"date_created": "2026-03-02T18:01:34.859000Z",
"date_modified": "2026-03-02T18:01:34.859000Z",
"file_hash": "5ec7fb626ee78a6992487379a8cf0b16596bd46720e00f51a899fdbd3bd1ae21",
"private": false,
"record": {
"abstract": "If a macromolecule is described by curvilinear coordinates or rigid\nconstraints are imposed, the equilibrium probability density that must be\nsampled in Monte Carlo simulations includes the determinants of different\nmass-metric tensors. In this work, we explicitly write the determinant of the\nmass-metric tensor G and of the reduced mass-metric tensor g, for any molecule,\ngeneral internal coordinates and arbitrary constraints, as a product of two\nfunctions; one depending only on the external coordinates that describe the\noverall translation and rotation of the system, and the other only on the\ninternal coordinates. This work extends previous results in the literature,\nproving with full generality that one may integrate out the external\ncoordinates and perform Monte Carlo simulations in the internal conformational\nspace of macromolecules. In addition, we give a general mathematical argument\nshowing that the factorization is a consequence of the symmetries of the metric\ntensors involved. Finally, the determinant of the mass-metric tensor G is\ncomputed explicitly in a set of curvilinear coordinates specially well-suited\nfor general branched molecules.",
"arxiv_id": "q-bio/0512033",
"authors": [
"Pablo Echenique",
"Ivan Calvo"
],
"categories": [
"q-bio.QM",
"cond-mat.soft"
],
"doi": "10.1002/jcc.20499",
"journal_ref": "J. Comp. Chem. 27 (2006) 1748-1755",
"title": "Explicit factorization of external coordinates in constrained Statistical Mechanics models",
"url": "https://arxiv.org/abs/q-bio/0512033"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "c4427e8d-4b99-4310-92c5-4111e9d8d766",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}