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Multi-configuration time-dependent Hartree
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<p>Multi-configuration time-dependent <a href="/facts/Douglas_Hartree/WKeyXHnK">Hartree</a> (MCTDH) is a general algorithm to solve the time-dependent <a href="/facts/Schr%25C3%25B6dinger_equation/3csgSIWF">Schrödinger equation</a> for multidimensional dynamical systems consisting of distinguishable <a href="/facts/Elementary_particle/CTFDM97U">particles</a>. MCTDH can thus determine the quantal motion of the nuclei of a <a href="/facts/Molecule/N9ljSfFq">molecular system</a> evolving on one or several <a href="/facts/Vibronic_coupling/IDmq1G4J">coupled</a> electronic <a href="/facts/Potential_energy_surface/YDUNcSM8">potential energy surfaces</a>. MCTDH by its very nature is an approximate method. However, it can be made as accurate as any competing method, but its numerical efficiency deteriorates with growing accuracy. </p><p>MCTDH is designed for multi-dimensional problems, in particular for problems that are difficult or even impossible to attack in a conventional way. There is no or only little gain when treating systems with less than three <a href="/facts/Degrees_of_freedom_(physics_and_chemistry)/Rrjl0lnq">degrees of freedom</a> by MCTDH. MCTDH will in general be best suited for systems with 4 to 12 degrees of freedom. Because of hardware limitations it may in general not be possible to treat much larger systems. For a certain class of problems, however, one can go much further. The MCTDH program package has recently been generalised to enable the propagation of <a href="/facts/Density_operator/A1XdylJa">density operators</a>. </p> <ul><li>Meyer, H.-D.; Manthe, U.; Cederbaum, L.S. (1990). "The multi-configurational time-dependent Hartree approach". <i>Chemical Physics Letters</i>. 165 (1). Elsevier BV: 73–78. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1990CPL...165...73M">1990CPL...165...73M</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1016%2F0009-2614%2890%2987014-i">10.1016/0009-2614(90)87014-i</a>. <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/0009-2614">0009-2614</a>.</li> <li>Manthe, U.; Meyer, H.‐D.; Cederbaum, L. S. (1992). "Wave‐packet dynamics within the multiconfiguration Hartree framework: General aspects and application to NOCl". <i>The Journal of Chemical Physics</i>. 97 (5). AIP Publishing: 3199–3213. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1992JChPh..97.3199M">1992JChPh..97.3199M</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1063%2F1.463007">10.1063/1.463007</a>. <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/0021-9606">0021-9606</a>.</li> <li>Beck, M. H.; Jäckle, A.; Worth, G. A.; Meyer, H.-D. (2000). "The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets". <i>Physics Reports</i>. 324 (1). Elsevier BV: 1–105. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2000PhR...324....1B">2000PhR...324....1B</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1016%2Fs0370-1573%2899%2900047-2">10.1016/s0370-1573(99)00047-2</a>. <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/0370-1573">0370-1573</a>.</li></ul>