Truncated Conjugate Gradient: An Optimal Strategy for the Analytical Evaluation of the Many-Body Polarization Energy and Forces in Molecular Simulations
We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in molecular simulations (i.e. molecular dynamics (MD) and Monte Carlo). The method consists in a fixed number of Conjugate Gradient (CG) iterations...
Saved in:
| Published in: | Journal of chemical theory and computation Vol. 13; no. 1; p. 180 |
|---|---|
| Main Authors: | , , , , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
United States
10.01.2017
|
| Subjects: | |
| ISSN: | 1549-9626, 1549-9626 |
| Online Access: | Get more information |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in molecular simulations (i.e. molecular dynamics (MD) and Monte Carlo). The method consists in a fixed number of Conjugate Gradient (CG) iterations. TCG approaches provide a scalable solution to the polarization problem at a user-chosen cost and a corresponding optimal accuracy. The optimality of the CG-method guarantees that the number of the required matrix-vector products are reduced to a minimum compared to other iterative methods. This family of methods is non-empirical, fully adaptive, and provides analytical gradients, avoiding therefore any energy drift in MD as compared to popular iterative solvers. Besides speed, one great advantage of this class of approximate methods is that their accuracy is systematically improvable. Indeed, as the CG-method is a Krylov subspace method, the associated error is monotonically reduced at each iteration. On top of that, two improvements can be proposed at virtually no cost: (i) the use of preconditioners can be employed, which leads to the Truncated Preconditioned Conjugate Gradient (TPCG); (ii) since the residual of the final step of the CG-method is available, one additional Picard fixed point iteration ("peek"), equivalent to one step of Jacobi Over Relaxation (JOR) with relaxation parameter ω, can be made at almost no cost. This method is denoted by TCG-n(ω). Black-box adaptive methods to find good choices of ω are provided and discussed. Results show that TPCG-3(ω) is converged to high accuracy (a few kcal/mol) for various types of systems including proteins and highly charged systems at the fixed cost of four matrix-vector products: three CG iterations plus the initial CG descent direction. Alternatively, T(P)CG-2(ω) provides robust results at a reduced cost (three matrix-vector products) and offers new perspectives for long polarizable MD as a production algorithm. The T(P)CG-1(ω) level provides less accurate solutions for inhomogeneous systems, but its applicability to well-conditioned problems such as water is remarkable, with only two matrix-vector product evaluations. |
|---|---|
| AbstractList | We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in molecular simulations (i.e. molecular dynamics (MD) and Monte Carlo). The method consists in a fixed number of Conjugate Gradient (CG) iterations. TCG approaches provide a scalable solution to the polarization problem at a user-chosen cost and a corresponding optimal accuracy. The optimality of the CG-method guarantees that the number of the required matrix-vector products are reduced to a minimum compared to other iterative methods. This family of methods is non-empirical, fully adaptive, and provides analytical gradients, avoiding therefore any energy drift in MD as compared to popular iterative solvers. Besides speed, one great advantage of this class of approximate methods is that their accuracy is systematically improvable. Indeed, as the CG-method is a Krylov subspace method, the associated error is monotonically reduced at each iteration. On top of that, two improvements can be proposed at virtually no cost: (i) the use of preconditioners can be employed, which leads to the Truncated Preconditioned Conjugate Gradient (TPCG); (ii) since the residual of the final step of the CG-method is available, one additional Picard fixed point iteration ("peek"), equivalent to one step of Jacobi Over Relaxation (JOR) with relaxation parameter ω, can be made at almost no cost. This method is denoted by TCG-n(ω). Black-box adaptive methods to find good choices of ω are provided and discussed. Results show that TPCG-3(ω) is converged to high accuracy (a few kcal/mol) for various types of systems including proteins and highly charged systems at the fixed cost of four matrix-vector products: three CG iterations plus the initial CG descent direction. Alternatively, T(P)CG-2(ω) provides robust results at a reduced cost (three matrix-vector products) and offers new perspectives for long polarizable MD as a production algorithm. The T(P)CG-1(ω) level provides less accurate solutions for inhomogeneous systems, but its applicability to well-conditioned problems such as water is remarkable, with only two matrix-vector product evaluations. We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in molecular simulations (i.e. molecular dynamics (MD) and Monte Carlo). The method consists in a fixed number of Conjugate Gradient (CG) iterations. TCG approaches provide a scalable solution to the polarization problem at a user-chosen cost and a corresponding optimal accuracy. The optimality of the CG-method guarantees that the number of the required matrix-vector products are reduced to a minimum compared to other iterative methods. This family of methods is non-empirical, fully adaptive, and provides analytical gradients, avoiding therefore any energy drift in MD as compared to popular iterative solvers. Besides speed, one great advantage of this class of approximate methods is that their accuracy is systematically improvable. Indeed, as the CG-method is a Krylov subspace method, the associated error is monotonically reduced at each iteration. On top of that, two improvements can be proposed at virtually no cost: (i) the use of preconditioners can be employed, which leads to the Truncated Preconditioned Conjugate Gradient (TPCG); (ii) since the residual of the final step of the CG-method is available, one additional Picard fixed point iteration ("peek"), equivalent to one step of Jacobi Over Relaxation (JOR) with relaxation parameter ω, can be made at almost no cost. This method is denoted by TCG-n(ω). Black-box adaptive methods to find good choices of ω are provided and discussed. Results show that TPCG-3(ω) is converged to high accuracy (a few kcal/mol) for various types of systems including proteins and highly charged systems at the fixed cost of four matrix-vector products: three CG iterations plus the initial CG descent direction. Alternatively, T(P)CG-2(ω) provides robust results at a reduced cost (three matrix-vector products) and offers new perspectives for long polarizable MD as a production algorithm. The T(P)CG-1(ω) level provides less accurate solutions for inhomogeneous systems, but its applicability to well-conditioned problems such as water is remarkable, with only two matrix-vector product evaluations.We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in molecular simulations (i.e. molecular dynamics (MD) and Monte Carlo). The method consists in a fixed number of Conjugate Gradient (CG) iterations. TCG approaches provide a scalable solution to the polarization problem at a user-chosen cost and a corresponding optimal accuracy. The optimality of the CG-method guarantees that the number of the required matrix-vector products are reduced to a minimum compared to other iterative methods. This family of methods is non-empirical, fully adaptive, and provides analytical gradients, avoiding therefore any energy drift in MD as compared to popular iterative solvers. Besides speed, one great advantage of this class of approximate methods is that their accuracy is systematically improvable. Indeed, as the CG-method is a Krylov subspace method, the associated error is monotonically reduced at each iteration. On top of that, two improvements can be proposed at virtually no cost: (i) the use of preconditioners can be employed, which leads to the Truncated Preconditioned Conjugate Gradient (TPCG); (ii) since the residual of the final step of the CG-method is available, one additional Picard fixed point iteration ("peek"), equivalent to one step of Jacobi Over Relaxation (JOR) with relaxation parameter ω, can be made at almost no cost. This method is denoted by TCG-n(ω). Black-box adaptive methods to find good choices of ω are provided and discussed. Results show that TPCG-3(ω) is converged to high accuracy (a few kcal/mol) for various types of systems including proteins and highly charged systems at the fixed cost of four matrix-vector products: three CG iterations plus the initial CG descent direction. Alternatively, T(P)CG-2(ω) provides robust results at a reduced cost (three matrix-vector products) and offers new perspectives for long polarizable MD as a production algorithm. The T(P)CG-1(ω) level provides less accurate solutions for inhomogeneous systems, but its applicability to well-conditioned problems such as water is remarkable, with only two matrix-vector product evaluations. |
| Author | Stamm, Benjamin Ponder, Jay W Aviat, Félix Maday, Yvon Piquemal, Jean-Philip Ren, Pengyu Lagardère, Louis Levitt, Antoine |
| Author_xml | – sequence: 1 givenname: Félix surname: Aviat fullname: Aviat, Félix organization: Laboratoire de Chimie Théorique, UPMC Université Paris 06, UMR 7617 , F-75005, Paris, France – sequence: 2 givenname: Antoine surname: Levitt fullname: Levitt, Antoine organization: Inria Paris, F-75589 Paris Cedex 12, Université Paris-Est, CERMICS (ENPC) , Marne-la-Vallée, F-77455, France – sequence: 3 givenname: Benjamin surname: Stamm fullname: Stamm, Benjamin organization: Computational Biomedicine, Institute for Advanced Simulation IAS-5 and Institute of Neuroscience and Medicine INM-9, Forschungszentrum Jülich , Jülich, 52425, Germany – sequence: 4 givenname: Yvon surname: Maday fullname: Maday, Yvon organization: Division of Applied Maths, Brown University , Providence, Rhode Island 02912, United States – sequence: 5 givenname: Pengyu surname: Ren fullname: Ren, Pengyu organization: Department of Biomedical Engineering, The University of Texas at Austin , Austin, Texas 78712, United States – sequence: 6 givenname: Jay W surname: Ponder fullname: Ponder, Jay W organization: Department of Chemistry, Washington University in Saint Louis , Campus Box 1134, One Brookings Drive, Saint Louis, Missouri 63130, United States – sequence: 7 givenname: Louis surname: Lagardère fullname: Lagardère, Louis organization: Institut du Calcul et de la Simulation, UPMC Université Paris 06 , F-75005, Paris, France – sequence: 8 givenname: Jean-Philip orcidid: 0000-0001-6615-9426 surname: Piquemal fullname: Piquemal, Jean-Philip organization: Institut Universitaire de France , Paris Cedex 05, 75231, France |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/28068773$$D View this record in MEDLINE/PubMed |
| BookMark | eNpNkM9LwzAAhYNM3KbePUmOXjrzo00bb3NsU1AUtntJk3R2dMlMUqH-Jf65RjfB03vwfbzDG4OBsUYDcIXRBCOCb4X0k60McsIqhHiBT8AIZylPOCNs8K8Pwdj7LUKUpoSegSEpECvynI7A19p1RoqgFZxZs-02scKlE6rRJtzBqYEv-9DsRAtXwUW26WFtHQxvOjLR9qGRkc0_RNuJ0FgDbf0Ln4Xpk3urevhqW-GazwOdG-3ihDAKLqyT2sPGwGfbatlFC66aXcwf01-A01q0Xl8e8xysF_P17CF5elk-zqZPicgQCklWsCpVnNc1JrmqVc1wxWmGVc1RkRcKxU5FynQqqyqluCoYkppnPDJGGTkHN4fZvbPvnfah3DVe6rYVRtvOl7jIcpozTkhUr49qV-20Kvcu_uL68u9M8g3oX3up |
| CitedBy_id | crossref_primary_10_1146_annurev_biophys_070317_033349 crossref_primary_10_1016_j_cie_2022_108656 crossref_primary_10_1039_C9SC01745C crossref_primary_10_3389_fmolb_2019_00143 crossref_primary_10_1016_j_cpc_2025_109700 crossref_primary_10_1002_wcms_1355 crossref_primary_10_1002_jcc_24830 crossref_primary_10_1002_jcc_25741 crossref_primary_10_1039_C9RA01983A crossref_primary_10_1016_j_polymer_2025_128559 crossref_primary_10_1039_D4RA07900K crossref_primary_10_48130_mpb_0025_0013 crossref_primary_10_1038_s41557_022_00977_2 crossref_primary_10_1007_s00371_025_04182_3 crossref_primary_10_1021_acs_jctc_5c00134 |
| ContentType | Journal Article |
| DBID | CGR CUY CVF ECM EIF NPM 7X8 |
| DOI | 10.1021/acs.jctc.6b00981 |
| DatabaseName | Medline MEDLINE MEDLINE (Ovid) MEDLINE MEDLINE PubMed MEDLINE - Academic |
| DatabaseTitle | MEDLINE Medline Complete MEDLINE with Full Text PubMed MEDLINE (Ovid) MEDLINE - Academic |
| DatabaseTitleList | MEDLINE MEDLINE - Academic |
| Database_xml | – sequence: 1 dbid: NPM name: PubMed url: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed sourceTypes: Index Database – sequence: 2 dbid: 7X8 name: MEDLINE - Academic url: https://search.proquest.com/medline sourceTypes: Aggregation Database |
| DeliveryMethod | no_fulltext_linktorsrc |
| Discipline | Chemistry |
| EISSN | 1549-9626 |
| ExternalDocumentID | 28068773 |
| Genre | Research Support, Non-U.S. Gov't Journal Article Research Support, N.I.H., Extramural |
| GrantInformation_xml | – fundername: NIGMS NIH HHS grantid: R01 GM114237 – fundername: NIGMS NIH HHS grantid: R01 GM106137 |
| GroupedDBID | 4.4 53G 55A 5GY 5VS 7~N AABXI ABBLG ABJNI ABLBI ABMVS ABQRX ABUCX ACGFS ACIWK ACS ADHLV AEESW AENEX AFEFF AHGAQ ALMA_UNASSIGNED_HOLDINGS AQSVZ BAANH CGR CS3 CUPRZ CUY CVF D0L DU5 EBS ECM ED~ EIF EJD F5P GGK GNL IH9 J9A JG~ NPM P2P RNS ROL UI2 VF5 VG9 W1F 7X8 |
| ID | FETCH-LOGICAL-a500t-586b4d99ff127dfdf61b9351df90878d03513a46e4cbb431b860ce95978d6362 |
| IEDL.DBID | 7X8 |
| ISICitedReferencesCount | 40 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000391898200017&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1549-9626 |
| IngestDate | Fri Jul 11 10:13:14 EDT 2025 Mon Jul 21 05:58:06 EDT 2025 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-a500t-586b4d99ff127dfdf61b9351df90878d03513a46e4cbb431b860ce95978d6362 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ORCID | 0000-0001-6615-9426 |
| OpenAccessLink | https://hal.science/hal-01395833 |
| PMID | 28068773 |
| PQID | 1857376922 |
| PQPubID | 23479 |
| ParticipantIDs | proquest_miscellaneous_1857376922 pubmed_primary_28068773 |
| PublicationCentury | 2000 |
| PublicationDate | 2017-01-10 |
| PublicationDateYYYYMMDD | 2017-01-10 |
| PublicationDate_xml | – month: 01 year: 2017 text: 2017-01-10 day: 10 |
| PublicationDecade | 2010 |
| PublicationPlace | United States |
| PublicationPlace_xml | – name: United States |
| PublicationTitle | Journal of chemical theory and computation |
| PublicationTitleAlternate | J Chem Theory Comput |
| PublicationYear | 2017 |
| References | 24459460 - J Chem Theory Comput. 2013 Dec 10;9(12):5430-5449 24901255 - J Phys Chem B. 2014 Jun 26;118(25):7156-66 26547155 - J Chem Phys. 2015 Nov 7;143(17):174104 26298123 - J Chem Phys. 2015 Aug 21;143(7):074115 27802661 - J Chem Phys. 2016 Oct 28;145(16):164101 20136072 - J Phys Chem B. 2010 Mar 4;114(8):2549-64 14696069 - J Comput Chem. 2004 Feb;25(3):335-42 24163642 - J Chem Theory Comput. 2013;9(9):4046-4063 26512230 - J Chem Theory Comput. 2014 Feb 28;10(4):1638-1651 16268681 - J Chem Phys. 2005 Oct 22;123(16):164107 26575557 - J Chem Theory Comput. 2015 Jun 9;11(6):2589-99 18978934 - J Chem Theory Comput. 2007 Nov;3(6):1960-1986 |
| References_xml | – reference: 26298123 - J Chem Phys. 2015 Aug 21;143(7):074115 – reference: 18978934 - J Chem Theory Comput. 2007 Nov;3(6):1960-1986 – reference: 26547155 - J Chem Phys. 2015 Nov 7;143(17):174104 – reference: 14696069 - J Comput Chem. 2004 Feb;25(3):335-42 – reference: 24901255 - J Phys Chem B. 2014 Jun 26;118(25):7156-66 – reference: 26575557 - J Chem Theory Comput. 2015 Jun 9;11(6):2589-99 – reference: 24459460 - J Chem Theory Comput. 2013 Dec 10;9(12):5430-5449 – reference: 16268681 - J Chem Phys. 2005 Oct 22;123(16):164107 – reference: 27802661 - J Chem Phys. 2016 Oct 28;145(16):164101 – reference: 24163642 - J Chem Theory Comput. 2013;9(9):4046-4063 – reference: 26512230 - J Chem Theory Comput. 2014 Feb 28;10(4):1638-1651 – reference: 20136072 - J Phys Chem B. 2010 Mar 4;114(8):2549-64 |
| SSID | ssj0033423 |
| Score | 2.391698 |
| Snippet | We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in... |
| SourceID | proquest pubmed |
| SourceType | Aggregation Database Index Database |
| StartPage | 180 |
| SubjectTerms | Algorithms Molecular Dynamics Simulation Monte Carlo Method Thermodynamics |
| Title | Truncated Conjugate Gradient: An Optimal Strategy for the Analytical Evaluation of the Many-Body Polarization Energy and Forces in Molecular Simulations |
| URI | https://www.ncbi.nlm.nih.gov/pubmed/28068773 https://www.proquest.com/docview/1857376922 |
| Volume | 13 |
| WOSCitedRecordID | wos000391898200017&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1La9tAEF7aOtBcmqSPxElTptDrJnqs95FLSY3dXuwY6oNvRqvdBQcipZYdyD_pz-3MWkpOhUIvOkhoEaPdmW9mdr-PsS-J9UJJlXLMZwVH_O-5yYXkwuRGKmmDLYsoNqGmU71YmFlbcGvabZWdT4yO2tUl1cgvibMIF4PJsq_3vzipRlF3tZXQeMl6OUIZmtVq8dRFyIndLvKlCmKhzLo2JYa1y6JsLm7LTXkhLVFqpn8HmDHQjA_-9xMP2ZsWYsL1bk4csRe-esteDztlt3fs93y9JS5Y72BYV7dbqqTB93Xc_LW5gusKbtCR3OEYLXftIyC0BYSKEDlMYvkbRk884VCH-HCCjoV_q90jzChhbk94wigeL4SicjCu1-iXYFXBpJPlhZ-ru1ZCrHnP5uPRfPiDtwoNnIQUNnygpRXOmBDSTLnggkytyQepCybRSjtqU-aFkF6U1iJUsVompTeYxGgnMXR-YK-quvInDIJPlU8l3hYDUfjM6MInzg98pq3Dwfvsc2fzJVqLuhpF5etts3y2ep8d737c8n7H1LGktrFWKj_9h7fP2H5GITuhLX4fWS_g8vfnbK982Kya9ac4s_A6nU3-AHb02vs |
| linkProvider | ProQuest |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Truncated+Conjugate+Gradient%3A+An+Optimal+Strategy+for+the+Analytical+Evaluation+of+the+Many-Body+Polarization+Energy+and+Forces+in+Molecular+Simulations&rft.jtitle=Journal+of+chemical+theory+and+computation&rft.au=Aviat%2C+F%C3%A9lix&rft.au=Levitt%2C+Antoine&rft.au=Stamm%2C+Benjamin&rft.au=Maday%2C+Yvon&rft.date=2017-01-10&rft.eissn=1549-9626&rft.volume=13&rft.issue=1&rft.spage=180&rft_id=info:doi/10.1021%2Facs.jctc.6b00981&rft_id=info%3Apmid%2F28068773&rft_id=info%3Apmid%2F28068773&rft.externalDocID=28068773 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1549-9626&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1549-9626&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1549-9626&client=summon |