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Starting from a Hartree product, all SPFs, except the first one, are unoccupied initially. To solve the MCTDH-EOMs numerically, one therefore has to remove the singularity by a regularization procedure. Usually the inverse of a density matrix is regularized. Here we argue and show that regularizing the coefficient tensor, which in turn regularizes the density matrix as well, leads to an improved performance of the EOMs. The initially unoccupied SPFs are rotated faster into their \u201ccorrect direction\u201d in Hilbert space and the final results are less sensitive to the choice of the value of the regularization parameter. For a particular example (a spin-boson system studied with a transformed Hamiltonian), we could even show that only with the new regularization scheme could one obtain correct results. Finally, in Appendix A, a new integration scheme for the MCTDH-EOMs developed by Lubich and co-workers is discussed. It is argued that this scheme does not solve the problem of the unoccupied natural orbitals because this scheme ignores the latter and does not propagate them at all.<\/jats:p>","DOI":"10.1063\/1.5024859","type":"journal-article","created":{"date-parts":[[2018,3,23]],"date-time":"2018-03-23T16:01:28Z","timestamp":1521820888000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":35,"title":["On regularizing the MCTDH equations of motion"],"prefix":"10.1063","volume":"148","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1365-0144","authenticated-orcid":false,"given":"Hans-Dieter","family":"Meyer","sequence":"first","affiliation":[{"name":"Physikalisch-Chemisches Institut, Universit\u00e4t Heidelberg 1 , Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haobin","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Chemistry, University of Colorado Denver 2 , Denver, Colorado 80217-3364, USA and , No. 10 East Xibeiwang Road, Haidian District, Beijing 100193, China"},{"name":"Beijing Computational Science Research Center 2 , Denver, Colorado 80217-3364, USA and , No. 10 East Xibeiwang Road, Haidian District, Beijing 100193, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2018,3,23]]},"reference":[{"key":"2023062000063263400_c1","doi-asserted-by":"publisher","first-page":"3199","DOI":"10.1063\/1.463007","article-title":"Wave-packet dynamics within the multiconfiguration Hartree framework: General aspects and application to NOCl","volume":"97","year":"1992","journal-title":"J. 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