Deep neural network for fitting analytical potential energy curve of diatomic molecules from ro-vibrational spectra

References

• Herzberg G. Molecular spectra and molecular structure: spectra of diatomic molecules. New York: Van Nostrand; 1950.
   Google Scholar
• Dunham JL. The energy levels of a rotating vibrator. Phys Rev. 1932;41:721–731.
   Google Scholar
• Kirschner SM, Watson JK. RKR potentials and semiclassical centrifugal constants of diatomic molecules. J Mol Spectrosc. 1973;47(2):234–242.
   Web of Science ®Google Scholar
• Le Roy RJ. RKR1: A computer program implementing the first-order RKR method for determining diatomic molecule potential energy functions. J Quant Spectrosc Radiat Transf. 2017;186:158–166.
   Web of Science ®Google Scholar
• Hurley A. Equivalence of Rydberg-Klein-Rees and simplified dunham potentials. J Chem Phys. 1962;36(4):1117–1118.
   Web of Science ®Google Scholar
• Rydberg R. Graphische darstellung einiger bandenspektroskopischer ergebnisse. Z Phys. 1932;73(5-6):376–385.
   Google Scholar
• Klein O. Zur berechnung von potentialkurven für zweiatomige moleküle mit hilfe von spektraltermen. Z Phys. 1932;76(3-4):226–235.
   Google Scholar
• Pashov A, Jackowska I, Jastrzebski W, et al. Polarization labeling spectroscopy of the 31Π and 61Σ+ states in NaK. Phys Rev A. 1998;58:1048–1054.
   Web of Science ®Google Scholar
• Kosman WM, Hinze J. Inverse perturbation analysis: improving the accuracy of potential energy curves. J Mol Spectrosc. 1975;56:93–103.
   Web of Science ®Google Scholar
• Pashov A, Jastrzȩbski W, Kowalczyk P. Construction of potential curves for diatomic molecular states by the IPA method. Comput Phys Commun. 2000;128:622–634.
   Web of Science ®Google Scholar
• Melville TC, Coxon JA. The application of direct potential fitting to the X1Σ+ ground electronic states of LiCl, TlCl, RbF and CsF. Spectrochim Acta A Mol Biomolecular Spectrosc. 2001;57(6):1171–1176.
   PubMed Web of Science ®Google Scholar
• Le Roy RJ. dPotFit: A computer program to fit diatomic molecule spectral data to potential energy functions. J Quant Spectrosc Radiat Transf. 2017;186:179–196.
   Web of Science ®Google Scholar
• Marques J, Prudente F, Pereira F, et al. A new genetic algorithm to be used in the direct fit of potential energy curves to ab initio and spectroscopic data. J Phys B Atom Molec Phys. 2008;41:085103.
   Web of Science ®Google Scholar
• Almeida MM, Prudente FV, Fellows CE, et al. Direct fit of spectroscopic data of diatomic molecules by using genetic algorithms: II. the ground state of RbCs. J Phys B. 2011;44:225102.
   Google Scholar
• Roncaratti L, Gargano R, Silva G. A genetic algorithm to build diatomic potentials. J Mol Struct (Theochem). 2006;769:47–51.
   Web of Science ®Google Scholar
• Bittencourt ACP, Prudente FV, Vianna JDM. The fitting of potential energy and transition moment functions using neural networks: transition probabilities in OH (A2Σ+→X2Π). Chem Phys. 2004;297(1):153–161.
   Web of Science ®Google Scholar
• Urbańczyk T, Koperski J. Neural networks and determination of diatomic molecule interatomic potential of cadmium dimer. Spectrochim Acta A. 2018;189:502–509.
   Web of Science ®Google Scholar
• Barber B, Zhang K, Guo B, et al. Vibration-Rotation emission spectrum of MgF. J Mol Spectrosc. 1995;169(2):583–589.
   Web of Science ®Google Scholar
• Abiodun OI, Jantan A, Omolara AE, et al. State-of-the-art in artificial neural network applications: A survey. Heliyon. 2018;4(11):e00938.
   PubMed Web of Science ®Google Scholar
• Krizhevsky A, Sutskever I, Hinton GE. ImageNet classification with deep convolutional neural networks. In: Proceedings of the 25th International Conference on Neural Information Processing Systems – Volume 1; NIPS'12. Red Hook (NY): Curran; 2012. p. 1097–1105
   Google Scholar
• Deng L, Hinton G, Kingsbury B. New types of deep neural network learning for speech recognition and related applications: an overview. In: 2013 IEEE Int Conf Acoust Speech Signal Process; 2013. p. 8599–8603.
   Google Scholar
• Gawehn E, Hiss JA, Brown JB, et al. Advancing drug discovery via GPU-based deep learning. Expert Opin Drug Discov. 2018;13(7):579–582.
   PubMed Web of Science ®Google Scholar
• Yu P, Yan X. Stock price prediction based on deep neural networks. Neural Comput Appl. 2020;32(6):1609–1628.
   Web of Science ®Google Scholar
• Moreira J, de Carvalho A, Horvath T. A general introduction to data analytics. Hoboken, NJ: Wiley–Interscience; 2018.
   Google Scholar
• Cybenko G. Approximation by superpositions of a sigmoidal function. Math Control Signals Syst. 1989;2:303–314.
   Google Scholar
• Maas AL, Hannun AY, Ng AY, Rectifier nonlinearities improve neural network acoustic models. In: ICML Workshop Deep Learn Audio Speech Lang Process. 2013;30.
   Google Scholar
• LeCun Y, Bengio Y, Hinton G. Deep learn. Nature. 2015;521:436–444.
   PubMed Web of Science ®Google Scholar
• Ramachandran P, Zoph B, Le QV. Searching for activation functions. abs/1710.05941. CoRR; 2017.
   Google Scholar
• Hahnloser R, Sarpeshkar R, Mahowald M, et al. Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit. Nature. 2000;405:947–951.
   PubMed Web of Science ®Google Scholar
• Glorot X, Bordes A, Bengio Y. Deep sparse rectifier neural networks. In: Gordon G, Dunson D, Dudík M, editors. Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics; Proceedings of Machine Learning Research; Vol. 15. PMLR; 2011. p. 315–323.
   Google Scholar
• Goodfellow I, Bengio Y, Courville A. Deep learning. Cambridge, MA: MIT Press; 2016.
   Google Scholar
• Svozil D, Kvasnicka V, Pospichal J. Introduction to multi-layer feed-forward neural networks. Chemom Intell Lab Syst. 1997;39(1):43–62.
   Web of Science ®Google Scholar
• Mittal S, Vaishay S. A survey of techniques for optimizing deep learning on GPUs. J Syst Architect. 2019;99:101635.
   Web of Science ®Google Scholar
• Hou S, Bernath PF. Line list for the mgF ground state. J Quant Spectrosc Radiat Transf. 2017;203:511–516.
   Web of Science ®Google Scholar
• Seto JY, Morbi Z, Charron F, et al. Vibration-rotation emission spectra and combined isotopomer analyses for the coinage metal hydrides: CuH & CuD, AgH & AgD, and AuH & AuD. J Chem Phys. 1999;110(24):11756–11767.
   Web of Science ®Google Scholar
• Le Roy RJ. LEVEL: A computer program for solving the radial Schrödinger equation for bound and quasibound levels. J Quant Spectrosc Radiat Transf. 2017;186:167–178.
   Web of Science ®Google Scholar
• Ioffe S, Szegedy C. Batch normalization: accelerating deep network training by reducing internal covariate shift. abs/1502.03167. CoRR; 2015.
   Google Scholar
• Douglas SC, Yu J. Why RELU units sometimes die: analysis of single-unit error backpropagation in neural networks. In: 2018 52nd Asilomar Conf Signals Syst Comput; 2018. p. 864–868.
   Google Scholar
• Lu L, Shin Y, Su Y, et al. Dying ReLU and initialization: theory and numerical examples. abs/1903.06733. CoRR; 2019.
   Google Scholar
• Chollet F. keras; 2015. Available from: https://github.com/fchollet/keras
   Google Scholar
• Bottou L. On-line Learning and Stochastic Approximations. In: Saad D., editor. On-Line Learning in Neural Networks (Publications of the Newton Institute). Cambridge: Cambridge University Press; 1999. p. 9–42. DOI:10.1017/CBO9780511569920.003.
   Google Scholar
• Kingma DP, Ba J. Adam: a method for stochastic optimization. abs/412.6980. International Conference on Learning Representations; 2015.
   Google Scholar
• Prechelt L. Automatic early stopping using cross validation: quantifying the criteria. Neural Netw. 1998;11(4):761–767.
   PubMed Web of Science ®Google Scholar
• He K, Zhang X, Ren S, et al. Delving deep into rectifiers: surpassing human-level performance on imageNet classification. In: IEEE Int Conf Comput Vis (ICCV 2015); 2015. p. 1502.
   Google Scholar
• Cunha W, Oliveira R, Roncaratti L, et al. Rovibrational energies and spectroscopic constants for H2O–Ng complexes. J Mol Model. 2014 12;20:2498.
   PubMed Web of Science ®Google Scholar
• Radzig AA, Smirnov BM. Reference data on atoms, molecules, and ions. Berlin, Heidelberg: Springer-Verlag; 1980.
   Google Scholar
• Czuchaj E, Krośnicki M. CCSD(T) calculation of the ground-state potential curves for the Cd-rare gas Van Der Waals molecules. Chem Phys Lett. 2000;329(5):495–502.
   Web of Science ®Google Scholar