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<title>Multi-configuration time-dependent Hartree</title>
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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Multi-configuration time-dependent Hartree</span></span>
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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="en" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p><b>Multi-configuration time-dependent <a href="Douglas_Hartree" title="Douglas Hartree">Hartree</a></b> (MCTDH) is a general algorithm to solve the time-dependent <a href="Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a> for multidimensional dynamical systems consisting of distinguishable <a href="Elementary_particle" title="Elementary particle">particles</a>. MCTDH can thus determine the quantal motion of the nuclei of a <a href="Molecule" title="Molecule">molecular system</a> evolving on one or several <a href="Vibronic_coupling" title="Vibronic coupling">coupled</a> electronic <a href="Potential_energy_surface" title="Potential energy surface">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="Degrees_of_freedom_(physics_and_chemistry)" title="Degrees of freedom (physics and chemistry)">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="Density_operator" class="mw-redirect" title="Density operator">density operators</a>.
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<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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</style><cite id="CITEREFMeyerMantheCederbaum1990" class="citation journal cs1">Meyer, H.-D.; Manthe, U.; Cederbaum, L.S. (1990). "The multi-configurational time-dependent Hartree approach". <i>Chemical Physics Letters</i>. <b>165</b> (1). Elsevier BV: <span class="nowrap">73–</span>78. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1990CPL...165...73M">1990CPL...165...73M</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0009-2614%2890%2987014-i">10.1016/0009-2614(90)87014-i</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0009-2614">0009-2614</a>.</cite></li>
<li><cite id="CITEREFMantheMeyerCederbaum1992" class="citation journal cs1">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>. <b>97</b> (5). AIP Publishing: <span class="nowrap">3199–</span>3213. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1992JChPh..97.3199M">1992JChPh..97.3199M</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.463007">10.1063/1.463007</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0021-9606">0021-9606</a>.</cite></li>
<li><cite id="CITEREFBeckJäckleWorthMeyer2000" class="citation journal cs1">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>. <b>324</b> (1). Elsevier BV: <span class="nowrap">1–</span>105. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000PhR...324....1B">2000PhR...324....1B</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fs0370-1573%2899%2900047-2">10.1016/s0370-1573(99)00047-2</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0370-1573">0370-1573</a>.</cite></li></ul>
<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>
<ul><li><a rel="nofollow" class="external text" href="http://mctdh.uni-hd.de">The Heidelberg MCTDH Homepage</a></li></ul>
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