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1. Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the United States

Author

Estee Y. Cramer, Evan L. Ray, Velma K. Lopez, Johannes Bracher, Andrea Brennen, Alvaro J. Castro Rivadeneira, Aaron Gerding, Tilmann Gneiting, Katie H. House, Yuxin Huang, Dasuni Jayawardena, Abdul H. Kanji, Ayush Khandelwal, Khoa Le, Anja Mühlemann, Jarad Niemi, Apurv Shah, Ariane Stark, Yijin Wang, Nutcha Wattanachit, Martha W. Zorn, Youyang Gu, Sansiddh Jain, Nayana Bannur, Ayush Deva, Mihir Kulkarni, Srujana Merugu, Alpan Raval, Siddhant Shingi, Avtansh Tiwari, Jerome White, Neil F. Abernethy, Spencer Woody, Maytal Dahan, Spencer Fox, Kelly Gaither, Michael Lachmann, Lauren Ancel Meyers, James G. Scott, Mauricio Tec, Ajitesh Srivastava, Glover E. George, Jeffrey C. Cegan, Ian D. Dettwiller, William P. England, Matthew W. Farthing, Robert H. Hunter, Brandon Lafferty, Igor Linkov, Michael L. Mayo, Matthew D. Parno, Michael A. Rowland, Benjamin D. Trump, Yanli Zhang-James, Samuel Chen, Stephen V. Faraone, Jonathan Hess, Christopher P. Morley, Asif Salekin, Dongliang Wang, Sabrina M. Corsetti, Thomas M. Baer, Marisa C. Eisenberg, Karl Falb, Yitao Huang, Emily T. Martin, Ella McCauley, Robert L. Myers, Tom Schwarz, Daniel Sheldon, Graham Casey Gibson, Rose Yu, Liyao Gao, Yian Ma, Dongxia Wu, Xifeng Yan, Xiaoyong Jin, Yu-Xiang Wang, YangQuan Chen, Lihong Guo, Yanting Zhao, Quanquan Gu, Jinghui Chen, Lingxiao Wang, Pan Xu, Weitong Zhang, Difan Zou, Hannah Biegel, Joceline Lega, Steve McConnell, V. P. Nagraj, Stephanie L. Guertin, Christopher Hulme-Lowe, Stephen D. Turner, Yunfeng Shi, Xuegang Ban, Robert Walraven, Qi-Jun Hong, Stanley Kong, Axel van de Walle, James A. Turtle, Michal Ben-Nun, Steven Riley, Pete Riley, Ugur Koyluoglu, David DesRoches, Pedro Forli, Bruce Hamory, Christina Kyriakides, Helen Leis, John Milliken, Michael Moloney, James Morgan, Ninad Nirgudkar, Gokce Ozcan, Noah Piwonka, Matt Ravi, Chris Schrader, Elizabeth Shakhnovich, Daniel Siegel, Ryan Spatz, Chris Stiefeling, Barrie Wilkinson, Alexander Wong, Sean Cavany, Guido España, Sean Moore, Rachel Oidtman, Alex Perkins, David Kraus, Andrea Kraus, Zhifeng Gao, Jiang Bian, Wei Cao, Juan Lavista Ferres, Chaozhuo Li, Tie-Yan Liu, Xing Xie, Shun Zhang, Shun Zheng, Alessandro Vespignani, Matteo Chinazzi, Jessica T. Davis, Kunpeng Mu, Ana Pastore y Piontti, Xinyue Xiong, Andrew Zheng, Jackie Baek, Vivek Farias, Andreea Georgescu, Retsef Levi, Deeksha Sinha, Joshua Wilde, Georgia Perakis, Mohammed Amine Bennouna, David Nze-Ndong, Divya Singhvi, Ioannis Spantidakis, Leann Thayaparan, Asterios Tsiourvas, Arnab Sarker, Ali Jadbabaie, Devavrat Shah, Nicolas Della Penna, Leo A. Celi, Saketh Sundar, Russ Wolfinger, Dave Osthus, Lauren Castro, Geoffrey Fairchild, Isaac Michaud, Dean Karlen, Matt Kinsey, Luke C. Mullany, Kaitlin Rainwater-Lovett, Lauren Shin, Katharine Tallaksen, Shelby Wilson, Elizabeth C. Lee, Juan Dent, Kyra H. Grantz, Alison L. Hill, Joshua Kaminsky, Kathryn Kaminsky, Lindsay T. Keegan, Stephen A. Lauer, Joseph C. Lemaitre, Justin Lessler, Hannah R. Meredith, Javier Perez-Saez, Sam Shah, Claire P. Smith, Shaun A. Truelove, Josh Wills, Maximilian Marshall, Lauren Gardner, Kristen Nixon, John C. Burant, Lily Wang, Lei Gao, Zhiling Gu, Myungjin Kim, Xinyi Li, Guannan Wang, Yueying Wang, Shan Yu, Robert C. Reiner, Ryan Barber, Emmanuela Gakidou, Simon I. Hay, Steve Lim, Chris Murray, David Pigott, Heidi L. Gurung, Prasith Baccam, Steven A. Stage, Bradley T. Suchoski, B. Aditya Prakash, Bijaya Adhikari, Jiaming Cui, Alexander Rodríguez, Anika Tabassum, Jiajia Xie, Pinar Keskinocak, John Asplund, Arden Baxter, Buse Eylul Oruc, Nicoleta Serban, Sercan O. Arik, Mike Dusenberry, Arkady Epshteyn, Elli Kanal, Long T. Le, Chun-Liang Li, Tomas Pfister, Dario Sava, Rajarishi Sinha, Thomas Tsai, Nate Yoder, Jinsung Yoon, Leyou Zhang, Sam Abbott, Nikos I. Bosse, Sebastian Funk, Joel Hellewell, Sophie R. Meakin, Katharine Sherratt, Mingyuan Zhou, Rahi Kalantari, Teresa K. Yamana, Sen Pei, Jeffrey Shaman, Michael L. Li, Dimitris Bertsimas, Omar Skali Lami, Saksham Soni, Hamza Tazi Bouardi, Turgay Ayer, Madeline Adee, Jagpreet Chhatwal, Ozden O. Dalgic, Mary A. Ladd, Benjamin P. Linas, Peter Mueller, Jade Xiao, Yuanjia Wang, Qinxia Wang, Shanghong Xie, Donglin Zeng, Alden Green, Jacob Bien, Logan Brooks, Addison J. Hu, Maria Jahja, Daniel McDonald, Balasubramanian Narasimhan, Collin Politsch, Samyak Rajanala, Aaron Rumack, Noah Simon, Ryan J. Tibshirani, Rob Tibshirani, Valerie Ventura, Larry Wasserman, Eamon B. O’Dea, John M. Drake, Robert Pagano, Quoc T. Tran, Lam Si Tung Ho, Huong Huynh, Jo W. Walker, Rachel B. Slayton, Michael A. Johansson, Matthew Biggerstaff, Nicholas G. Reich, Cramer, Estee Y [0000-0003-1373-3177], Ray, Evan L [0000-0003-4035-0243], Lopez, Velma K [0000-0003-2926-4010], Bracher, Johannes [0000-0002-3777-1410], Gneiting, Tilmann [0000-0001-9397-3271], Niemi, Jarad [0000-0002-5079-158X], White, Jerome [0000-0003-4148-8834], Woody, Spencer [0000-0002-2882-3450], Fox, Spencer [0000-0003-1969-3778], Gaither, Kelly [0000-0002-4272-175X], Meyers, Lauren Ancel [0000-0002-5828-8874], Tec, Mauricio [0000-0002-1853-5842], George, Glover E [0000-0003-4779-8702], Cegan, Jeffrey C [0000-0002-3065-3403], Hunter, Robert H [0000-0002-2382-7938], Lafferty, Brandon [0000-0002-2618-3787], Mayo, Michael L [0000-0001-9014-1859], Rowland, Michael A [0000-0002-6759-8225], Chen, Samuel [0000-0002-1070-9801], Salekin, Asif [0000-0002-0807-8967], Corsetti, Sabrina M [0000-0003-2216-2492], Falb, Karl [0000-0002-3465-3988], Huang, Yitao [0000-0001-7846-2174], Sheldon, Daniel [0000-0002-4257-2432], Guo, Lihong [0000-0003-4804-4005], Gu, Quanquan [0000-0001-9830-793X], Xu, Pan [0000-0002-2559-8622], Lega, Joceline [0000-0003-2064-229X], McConnell, Steve [0000-0002-0294-3737], Turner, Stephen D [0000-0001-9140-9028], Shi, Yunfeng [0000-0003-1700-6049], Walraven, Robert [0000-0002-5755-4325], van de Walle, Axel [0000-0002-3415-1494], Turtle, James A [0000-0003-0735-7769], Ben-Nun, Michal [0000-0002-9164-0008], Riley, Steven [0000-0001-7904-4804], Koyluoglu, Ugur [0000-0002-6286-351X], Cavany, Sean [0000-0002-2559-797X], España, Guido [0000-0002-9915-8056], Moore, Sean [0000-0001-9062-6100], Oidtman, Rachel [0000-0003-1773-9533], Perkins, Alex [0000-0002-7518-4014], Kraus, David [0000-0003-4376-3932], Cao, Wei [0000-0001-5640-0917], Lavista Ferres, Juan [0000-0002-9654-3178], Vespignani, Alessandro [0000-0003-3419-4205], Sinha, Deeksha [0000-0002-9788-728X], Perakis, Georgia [0000-0002-0888-9030], Bennouna, Mohammed Amine [0000-0002-9123-8588], Spantidakis, Ioannis [0000-0002-5149-6320], Tsiourvas, Asterios [0000-0002-2979-6300], Sarker, Arnab [0000-0003-1680-9421], Jadbabaie, Ali [0000-0003-1122-3069], Shah, Devavrat [0000-0003-0737-3259], Celi, Leo A [0000-0001-6712-6626], Osthus, Dave [0000-0002-4681-091X], Fairchild, Geoffrey [0000-0001-5500-8120], Mullany, Luke C [0000-0003-4668-9803], Rainwater-Lovett, Kaitlin [0000-0002-8707-7339], Lee, Elizabeth C [0000-0002-4156-9637], Dent, Juan [0000-0003-3154-0731], Hill, Alison L [0000-0002-6583-3623], Keegan, Lindsay T [0000-0002-8526-3007], Lemaitre, Joseph C [0000-0002-2677-6574], Truelove, Shaun A [0000-0003-0538-0607], Wills, Josh [0000-0001-7285-9349], Gao, Lei [0000-0002-4707-0933], Gu, Zhiling [0000-0002-8052-7608], Yu, Shan [0000-0002-0271-5726], Hay, Simon I [0000-0002-0611-7272], Murray, Chris [0000-0002-4930-9450], Stage, Steven A [0000-0001-5361-6464], Prakash, B Aditya [0000-0002-3252-455X], Rodríguez, Alexander [0000-0002-4313-9913], Xie, Jiajia [0000-0001-6530-2489], Keskinocak, Pinar [0000-0003-2686-546X], Baxter, Arden [0000-0002-6345-2229], Oruc, Buse Eylul [0000-0003-2431-3864], Sinha, Rajarishi [0000-0001-9157-674X], Yoder, Nate [0000-0003-4153-4722], Zhang, Leyou [0000-0002-2454-0082], Funk, Sebastian [0000-0002-2842-3406], Meakin, Sophie R [0000-0002-6385-2652], Sherratt, Katharine [0000-0003-2049-3423], Yamana, Teresa K [0000-0001-8349-3151], Pei, Sen [0000-0002-7072-2995], Shaman, Jeffrey [0000-0002-7216-7809], Li, Michael L [0000-0002-2456-4834], Bertsimas, Dimitris [0000-0002-1985-1003], Skali Lami, Omar [0000-0002-8208-3035], Soni, Saksham [0000-0002-8898-5726], Tazi Bouardi, Hamza [0000-0002-7871-325X], Wang, Yuanjia [0000-0002-1510-3315], McDonald, Daniel [0000-0002-0443-4282], Politsch, Collin [0000-0003-3727-9167], Rajanala, Samyak [0000-0002-5791-3789], Rumack, Aaron [0000-0002-9181-1794], Tibshirani, Ryan J [0000-0002-2158-8304], Drake, John M [0000-0003-4646-1235], Ho, Lam Si Tung [0000-0002-0453-8444], Slayton, Rachel B [0000-0003-4699-8040], Johansson, Michael A [0000-0002-5090-7722], Biggerstaff, Matthew [0000-0001-5108-8311], Reich, Nicholas G [0000-0003-3503-9899], and Apollo - University of Cambridge Repository

Subjects
model evaluation, Multidisciplinary, COVID-19, prediction, United States, Data Accuracy, 510 Mathematics, 360 Social problems & social services, weather, Humans, Public Health, ddc:510, ensemble forecast, Pandemics, Mathematics, Forecasting, Probability
Abstract

Short-term probabilistic forecasts of the trajectory of the COVID-19 pandemic in the United States have served as a visible and important communication channel between the scientific modeling community and both the general public and decision-makers. Forecasting models provide specific, quantitative, and evaluable predictions that inform short-term decisions such as healthcare staffing needs, school closures, and allocation of medical supplies. Starting in April 2020, the US COVID-19 Forecast Hub ( https://covid19forecasthub.org/ ) collected, disseminated, and synthesized tens of millions of specific predictions from more than 90 different academic, industry, and independent research groups. A multimodel ensemble forecast that combined predictions from dozens of groups every week provided the most consistently accurate probabilistic forecasts of incident deaths due to COVID-19 at the state and national level from April 2020 through October 2021. The performance of 27 individual models that submitted complete forecasts of COVID-19 deaths consistently throughout this year showed high variability in forecast skill across time, geospatial units, and forecast horizons. Two-thirds of the models evaluated showed better accuracy than a naïve baseline model. Forecast accuracy degraded as models made predictions further into the future, with probabilistic error at a 20-wk horizon three to five times larger than when predicting at a 1-wk horizon. This project underscores the role that collaboration and active coordination between governmental public-health agencies, academic modeling teams, and industry partners can play in developing modern modeling capabilities to support local, state, and federal response to outbreaks.

Published
2022
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2. Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the US

Author

Estee Y Cramer, Evan L Ray, Velma K Lopez, Johannes Bracher, Andrea Brennen, Alvaro J Castro Rivadeneira, Aaron Gerding, Tilmann Gneiting, Katie H House, Yuxin Huang, Dasuni Jayawardena, Abdul H Kanji, Ayush Khandelwal, Khoa Le, Anja Mühlemann, Jarad Niemi, Apurv Shah, Ariane Stark, Yijin Wang, Nutcha Wattanachit, Martha W Zorn, Youyang Gu, Sansiddh Jain, Nayana Bannur, Ayush Deva, Mihir Kulkarni, Srujana Merugu, Alpan Raval, Siddhant Shingi, Avtansh Tiwari, Jerome White, Neil F Abernethy, Spencer Woody, Maytal Dahan, Spencer Fox, Kelly Gaither, Michael Lachmann, Lauren Ancel Meyers, James G Scott, Mauricio Tec, Ajitesh Srivastava, Glover E George, Jeffrey C Cegan, Ian D Dettwiller, William P England, Matthew W Farthing, Robert H Hunter, Brandon Lafferty, Igor Linkov, Michael L Mayo, Matthew D Parno, Michael A Rowland, Benjamin D Trump, Yanli Zhang-James, Samuel Chen, Stephen V Faraone, Jonathan Hess, Christopher P Morley, Asif Salekin, Dongliang Wang, Sabrina M Corsetti, Thomas M Baer, Marisa C Eisenberg, Karl Falb, Yitao Huang, Emily T Martin, Ella McCauley, Robert L Myers, Tom Schwarz, Daniel Sheldon, Graham Casey Gibson, Rose Yu, Liyao Gao, Yian Ma, Dongxia Wu, Xifeng Yan, Xiaoyong Jin, Yu-Xiang Wang, YangQuan Chen, Lihong Guo, Yanting Zhao, Quanquan Gu, Jinghui Chen, Lingxiao Wang, Pan Xu, Weitong Zhang, Difan Zou, Hannah Biegel, Joceline Lega, Steve McConnell, VP Nagraj, Stephanie L Guertin, Christopher Hulme-Lowe, Stephen D Turner, Yunfeng Shi, Xuegang Ban, Robert Walraven, Qi-Jun Hong, Stanley Kong, Axel van de Walle, James A Turtle, Michal Ben-Nun, Steven Riley, Pete Riley, Ugur Koyluoglu, David DesRoches, Pedro Forli, Bruce Hamory, Christina Kyriakides, Helen Leis, John Milliken, Michael Moloney, James Morgan, Ninad Nirgudkar, Gokce Ozcan, Noah Piwonka, Matt Ravi, Chris Schrader, Elizabeth Shakhnovich, Daniel Siegel, Ryan Spatz, Chris Stiefeling, Barrie Wilkinson, Alexander Wong, Sean Cavany, Guido España, Sean Moore, Rachel Oidtman, Alex Perkins, David Kraus, Andrea Kraus, Zhifeng Gao, Jiang Bian, Wei Cao, Juan Lavista Ferres, Chaozhuo Li, Tie-Yan Liu, Xing Xie, Shun Zhang, Shun Zheng, Alessandro Vespignani, Matteo Chinazzi, Jessica T Davis, Kunpeng Mu, Ana Pastore y Piontti, Xinyue Xiong, Andrew Zheng, Jackie Baek, Vivek Farias, Andreea Georgescu, Retsef Levi, Deeksha Sinha, Joshua Wilde, Georgia Perakis, Mohammed Amine Bennouna, David Nze-Ndong, Divya Singhvi, Ioannis Spantidakis, Leann Thayaparan, Asterios Tsiourvas, Arnab Sarker, Ali Jadbabaie, Devavrat Shah, Nicolas Della Penna, Leo A Celi, Saketh Sundar, Russ Wolfinger, Dave Osthus, Lauren Castro, Geoffrey Fairchild, Isaac Michaud, Dean Karlen, Matt Kinsey, Luke C. Mullany, Kaitlin Rainwater-Lovett, Lauren Shin, Katharine Tallaksen, Shelby Wilson, Elizabeth C Lee, Juan Dent, Kyra H Grantz, Alison L Hill, Joshua Kaminsky, Kathryn Kaminsky, Lindsay T Keegan, Stephen A Lauer, Joseph C Lemaitre, Justin Lessler, Hannah R Meredith, Javier Perez-Saez, Sam Shah, Claire P Smith, Shaun A Truelove, Josh Wills, Maximilian Marshall, Lauren Gardner, Kristen Nixon, John C. Burant, Lily Wang, Lei Gao, Zhiling Gu, Myungjin Kim, Xinyi Li, Guannan Wang, Yueying Wang, Shan Yu, Robert C Reiner, Ryan Barber, Emmanuela Gakidou, Simon I. Hay, Steve Lim, Chris J.L. Murray, David Pigott, Heidi L Gurung, Prasith Baccam, Steven A Stage, Bradley T Suchoski, B. Aditya Prakash, Bijaya Adhikari, Jiaming Cui, Alexander Rodríguez, Anika Tabassum, Jiajia Xie, Pinar Keskinocak, John Asplund, Arden Baxter, Buse Eylul Oruc, Nicoleta Serban, Sercan O Arik, Mike Dusenberry, Arkady Epshteyn, Elli Kanal, Long T Le, Chun-Liang Li, Tomas Pfister, Dario Sava, Rajarishi Sinha, Thomas Tsai, Nate Yoder, Jinsung Yoon, Leyou Zhang, Sam Abbott, Nikos I Bosse, Sebastian Funk, Joel Hellewell, Sophie R Meakin, Katharine Sherratt, Mingyuan Zhou, Rahi Kalantari, Teresa K Yamana, Sen Pei, Jeffrey Shaman, Michael L Li, Dimitris Bertsimas, Omar Skali Lami, Saksham Soni, Hamza Tazi Bouardi, Turgay Ayer, Madeline Adee, Jagpreet Chhatwal, Ozden O Dalgic, Mary A Ladd, Benjamin P Linas, Peter Mueller, Jade Xiao, Yuanjia Wang, Qinxia Wang, Shanghong Xie, Donglin Zeng, Alden Green, Jacob Bien, Logan Brooks, Addison J Hu, Maria Jahja, Daniel McDonald, Balasubramanian Narasimhan, Collin Politsch, Samyak Rajanala, Aaron Rumack, Noah Simon, Ryan J Tibshirani, Rob Tibshirani, Valerie Ventura, Larry Wasserman, Eamon B O’Dea, John M Drake, Robert Pagano, Quoc T Tran, Lam Si Tung Ho, Huong Huynh, Jo W Walker, Rachel B Slayton, Michael A Johansson, Matthew Biggerstaff, and Nicholas G Reich

Subjects
Geospatial analysis, Coronavirus disease 2019 (COVID-19), Computer science, business.industry, Probabilistic logic, Staffing, computer.software_genre, Scientific modelling, Health care, Econometrics, National level, business, computer, Independent research
Abstract

Short-term probabilistic forecasts of the trajectory of the COVID-19 pandemic in the United States have served as a visible and important communication channel between the scientific modeling community and both the general public and decision-makers. Forecasting models provide specific, quantitative, and evaluable predictions that inform short-term decisions such as healthcare staffing needs, school closures, and allocation of medical supplies. Starting in April 2020, the US COVID-19 Forecast Hub (https://covid19forecasthub.org/) collected, disseminated, and synthesized tens of millions of specific predictions from more than 90 different academic, industry, and independent research groups. A multi-model ensemble forecast that combined predictions from dozens of different research groups every week provided the most consistently accurate probabilistic forecasts of incident deaths due to COVID-19 at the state and national level from April 2020 through October 2021. The performance of 27 individual models that submitted complete forecasts of COVID-19 deaths consistently throughout this year showed high variability in forecast skill across time, geospatial units, and forecast horizons. Two-thirds of the models evaluated showed better accuracy than a naïve baseline model. Forecast accuracy degraded as models made predictions further into the future, with probabilistic error at a 20-week horizon 3-5 times larger than when predicting at a 1-week horizon. This project underscores the role that collaboration and active coordination between governmental public health agencies, academic modeling teams, and industry partners can play in developing modern modeling capabilities to support local, state, and federal response to outbreaks. Significance Statement This paper compares the probabilistic accuracy of short-term forecasts of reported deaths due to COVID-19 during the first year and a half of the pandemic in the US. Results show high variation in accuracy between and within stand-alone models, and more consistent accuracy from an ensemble model that combined forecasts from all eligible models. This demonstrates that an ensemble model provided a reliable and comparatively accurate means of forecasting deaths during the COVID-19 pandemic that exceeded the performance of all of the models that contributed to it. This work strengthens the evidence base for synthesizing multiple models to support public health action.

Published
2021
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3. An adaptable discrete variable representation based on coherent states

Author

John C. Burant

Subjects
Basis (linear algebra), Discretization, Computer science, Phase space, Singular value decomposition, General Physics and Astronomy, Coherent states, Orthonormal basis, Physical and Theoretical Chemistry, Representation (mathematics), Algorithm, Eigenvalues and eigenvectors
Abstract

A novel approach for constructing a discrete variable representation (DVR) is described. The procedure involves two basis transformations. A finite, nonorthogonal, and overcomplete coherent state (CS) basis is transformed to an orthonormal basis via singular value decomposition (SVD). This orthonormal basis is then transformed to a DVR in the usual manner. This DVR is easily optimized for specific problems by restricting CS to relevant phase space regions. The SVD allows one to tailor the desired level of accuracy uniformly over the entire desired energy range. The method is illustrated with application to a two-dimensional Henon–Heiles potential.

Published
2002
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4. Real time path integrals using the Herman–Kluk propagator

Author

Victor S. Batista and John C. Burant

Subjects
Matrix (mathematics), Quantum dynamics, Quantum process, Quantum mechanics, Quantum operation, General Physics and Astronomy, Initial value problem, Semiclassical physics, Propagator, Limit (mathematics), Statistical physics, Physical and Theoretical Chemistry, Mathematics
Abstract

It is shown that the accuracy of quantum dynamics calculations obtained according to the Herman–Kluk (HK) semiclassical initial value representation (SC-IVR) is significantly improved when the time evolution operator is computed by concatenating finite time propagators. This approach results in an approximate calculation of a real-time path-integral in a discrete coherent-state representation, which becomes exact in the limit of sufficiently short time-slice intervals. The efficiency of the computational method is optimized by devising a compact coherent-state basis set that obviates the need for calculating the inverse overlap matrix. Quantitative agreement with full quantum mechanical results is verified in the description of tunneling between disjoint classically allowed regions in one- and two-dimensional systems, in the treatment of long-time dynamics, and in nonadiabatic dynamics in a model system with two coupled one-dimensional potential energy surfaces.

Published
2002
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5. Nonadiabatic dynamics via the classical limit Schrödinger equation

Author

John C. Burant and John C. Tully

Subjects
Physics, Quantum mechanics, Quantum dynamics, Master equation, Quantum potential, General Physics and Astronomy, Method of quantum characteristics, Correspondence principle, Surface hopping, Physical and Theoretical Chemistry, Quantum dissipation, Classical limit
Abstract

The coupled Schrodinger equations that describe nonadiabatic dynamics are recast using the Bohm formulation of quantum mechanics. The resulting coupled Bohm equations are solved numerically for two scattering models, giving results that are essentially identical to wave-packet solution of the original coupled Schrodinger equations. The classical limit of the set of coupled Bohm equations is then described, producing a mixed quantum-classical theory incorporating classical-like motion on each potential energy surface accompanied by quantum transitions between the quantum states. Numerical tests of the mixed quantum-classical method are in excellent agreement with the accurate full-quantum results for the model problems. The method is contrasted with the related surface-hopping approach. It is shown that computing the dynamics of a distribution of classical particles is more consistent and more accurate than computing the motion of independent point particles as with surface hopping.

Published
2000
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6. Improving harmonic vibrational frequencies calculations in density functional theory

Author

John C. Burant, Gustavo E. Scuseria, Michael J. Frisch, and R. Eric Stratmann

Subjects
Chemistry, Fast multipole method, Gaussian, General Physics and Astronomy, Computational physics, Numerical integration, Quadrature (mathematics), symbols.namesake, Quantum mechanics, symbols, Harmonic, Density functional theory, Physical and Theoretical Chemistry, Multipole expansion, Order of magnitude
Abstract

Using a previously introduced weight scheme, microbatching, and grid compression [R. E. Stratmann, G. E. Scuseria and M. J. Frisch, Chem. Phys. Lett. 257, 213 (1996)], we significantly speed up the numerical integration of the exchange-correlation contribution to the Coupled-Perturbed Kohn–Sham equations. In addition, we find that the nature of the integrand is such that it is possible to employ substantially fewer grid points in the quadrature and to use the Gaussian very Fast Multipole Method (GvFMM) with very short multipole expansions for the Coulomb contribution, with negligible loss in accuracy. As a representative example, the computational demand for the exchange-correlation portion of a coronene (C24H12) frequency calculation with a 3-21G basis is reduced by more than one order of magnitude. The overall speed up achieved in this calculation is between a factor of 4 to 6, depending on the specific functional. We also present sample calculations using polarized bases, gradient-corrected functionals, and on even larger systems (C54H18 and C96H24), to illustrate the various effects and improvements that we have accomplished.

Published
1997
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7. A linear scaling method for Hartree–Fock exchange calculations of large molecules

Author

Gustavo E. Scuseria, John C. Burant, and Michael J. Frisch

Subjects
Chemistry, Hartree–Fock method, General Physics and Astronomy, Charge density, Diamond, Time scaling, engineering.material, Calculation methods, Linear scale, engineering, Molecule, Physical and Theoretical Chemistry, Atomic physics, Scaling
Abstract

We introduce the near‐field exchange method for calculating Hartree–Fock exchange in time scaling near‐linearly with system size. Benchmarks on polyglycine chains, water clusters, and diamond pieces show that microhartree accuracy and substantial speedups (up to 10×) over traditional calculations can be obtained for electrically insulating systems larger than 300 atoms.

Published
1996
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8. Kohn-Sham analytic energy second derivatives with the Gaussian very fast multipole method (GvFMM)

Author

Michael J. Frisch, Gustavo E. Scuseria, Matthew C. Strain, and John C. Burant

Subjects
Physics, Fast multipole method, Gaussian, General Physics and Astronomy, Kohn–Sham equations, Basis function, Matrix (mathematics), symbols.namesake, Computational chemistry, Quantum mechanics, Coulomb, symbols, Density functional theory, Physical and Theoretical Chemistry, Second derivative
Abstract

The first application of the Gaussian very fast multipole method (GvFMM) to the calculation of molecular energy second derivatives of Kohn-Sham (KS) density functional theory (DFT) is reported. The GvFMM is used both in the solution of the coupled-perturbed KS (CPKS) equations and in the calculation of electron-electron repulsion integral second derivatives. We present benchmark tests on C24H12 and C54H18 using 3-21G and 6-31G∗ basis sets that show modest improvements of speed for the formation of J(x) (the Coulomb matrix formed from derivatives of the basis functions) and the integral second derivatives.

Published
1996
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9. Analytic energy gradients for the Gaussian very fast multipole method (GvFMM)

Author

Gustavo E. Scuseria, John C. Burant, Matthew C. Strain, and Michael J. Frisch

Subjects
Physics, Energy gradient, Fast multipole method, Gaussian, General Physics and Astronomy, Hartree, Bohr model, Computational physics, symbols.namesake, Classical mechanics, Coulomb, symbols, Physical and Theoretical Chemistry, Scaling, Energy (signal processing)
Abstract

The first use of the Gaussian very fast multipole method (GvFMM) for calculating the integral derivatives that arise in the Coulomb terms of density-functional theory (DFT) energy gradients is reported. Tests of the GvFMM gradient algorithm indicate that its accuracy, speed, and near-linear scaling behavior are similar to the GvFMM molecular energy algorithm. Specifically, 10−8 hartree per Bohr accuracy in the energy gradient has been achieved, and the ratio of the computational cost for the GvFMM energy gradient to the GvFMM energy has been found to be lower than the ratio for previous state-of-the-art method.

Published
1996
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