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The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm\u22121 and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.<\/jats:p>","DOI":"10.1063\/1.4892614","type":"journal-article","created":{"date-parts":[[2014,8,25]],"date-time":"2014-08-25T20:30:33Z","timestamp":1408998633000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":14,"title":["Stochastic many-body perturbation theory for anharmonic molecular vibrations"],"prefix":"10.1063","volume":"141","author":[{"given":"Matthew R.","family":"Hermes","sequence":"first","affiliation":[{"name":"University of Illinois at Urbana-Champaign 1 Department of Chemistry, , 600 South Mathews Avenue, Urbana, Illinois 61801, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"So","family":"Hirata","sequence":"additional","affiliation":[{"name":"University of Illinois at Urbana-Champaign 1 Department of Chemistry, , 600 South Mathews Avenue, Urbana, Illinois 61801, USA"},{"name":"CREST 2 , Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2014,8,25]]},"reference":[{"key":"2023070323370795700_c1","doi-asserted-by":"publisher","first-page":"2145","DOI":"10.1080\/00268970802258609","volume":"106","year":"2008","journal-title":"Mol. 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