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Electron correlation plays an important role in the multielectron interactions of many physical and chemical processes.The investigation of correlation effects in the non-perturbative electronic dynamics (e.g.non-sequential double ionization) when atoms and molecules are subjected to strong laser fields requires non-perturbative theoretical treatments. The direct numerical integration of the time-dependent Schrödinger equation successfully explains many experimental results,but it is computationally prohibitive for systems with more than two electrons.There is clearly a need for a theory which can treat correlation dynamics self-consistently in strong time-dependent electric fields.In this paper we develop a three-dimensional multiconfiguration time-dependent Hartree-Fock method,which can be applied to the non-perturbative electronic dynamics for diatomic molecules,and it can also investigate the effect of electron correlation in strong-field ionization of H2 molecules.This method adopts the prolate spheroidal coordinates (which can treat the two-center Coulomb potential accurately) and the finite-element method together with discrete-variable representation (which lowers the calculation burden from two-electron integrations).For the temporal propagation,we use the efficient short iterative Lanczos algorithm for the equation which governs the configuration expansion coefficients,while an eight-order Runge-Kutta (RK) method and an Bulirsch-Stoer (BS) extrapolation method,both with adaptive precision controls,are implemented to solve the nonlinear orbital equation.While both methods yield correct results,the BS method displays a better stability in the realtime propagation,while the RK method demands less computation.The alignment-dependent ionization probabilities of H2 molecules in intense extreme ultraviolet pulses are calculated.Comparisons between multi-configuration and single-configuration results show that electron correlation has little effect on the single ionization process,but it plays an important role in double ionization,leading to the decrease in the ionization probability.The double ionization probability from the single-configuration space 1σ is about three times larger that from 4σ1π.The ionization probability increases monotonically when the alignment angle increases from 0° to 90°, yielding a ratio of 2.6(1.5) between 90° and 0° for the double (single) ionization process.This method presents the basis for the future study of electron correlation in strong-field processes.
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Keywords:
- multiconfiguration time-dependent Hartree-Fock /
- electron correlation /
- strong-field ionization /
- hydrogen molecules
[1] Xu G X, Li L M, Wang D M, Chen M B 2009 Quantum Chemistry:Fundamental Principle and Ab-initio Calculation Method (2nd Ed.) (Vol. 1) (Beijing:Science Press) pp869-874 (in Chinese)[徐光宪, 黎乐民, 王德民, 陈敏伯 2009 量子化学——基本原理和从头计算法(下) (第二版)(北京:科学出版社) 第869–874页]
[2] Becker W, Liu X J, Ho P J, Eberly J H 2012 Rev. Mod. Phys. 84 1011
[3] Zhao L, Zhang Q, Dong J W, L H, Xu H F 2016 Acta Phys. Sin. 65 223201 (in Chinese)[赵磊, 张琦, 董敬伟, 吕航, 徐海峰 2016 物理学报 65 223201]
[4] Jin F C, Wang B B 2016 Acta Phys. Sin. 65 224205 (in Chinese)[金发成, 王兵兵 2016 物理学报 65 224205]
[5] Hu S X 2013 Phys. Rev. Lett. 111 123003
[6] Ye D F, Liu X, Liu J 2008 Phys. Rev. Lett. 101 233003
[7] Brabec T, Krausz F 2000 Rev. Mod. Phys. 72 545
[8] Posthumus J H 2004 Rep. Progr. Phys. 67 623
[9] Xiao X R, Wang M X, Li M, Geng J W, Liu Y Q, Peng L Y 2016 Acta Phys. Sin. 65 220203 (in Chinese)[肖相如, 王慕雪, 黎敏, 耿基伟, 刘运全, 彭良友 2016 物理学报 65 220203]
[10] Zhang Z, Peng L Y, Xu M H, Starace A F, Morishita T, Gong Q H 2011 Phys. Rev. A 84 043409
[11] Guan X, Bartschat K, Schneider B I 2011 Phys. Rev. A 83 043403
[12] Stapelfeldt H 2003 Rev. Mod. Phys. 75 543
[13] Kulander K 1987 Phys. Rev. A 36 2726
[14] Marques M A L, Ullrich C A, Nogueira F, Rubio A, Burke K, Gross E K U 2006 Time-Dependent Density Functional Theory (Heidelberg, Berlin:Springer) pp1-13
[15] Hochstuhl D, Bonitz M 2012 Phys. Rev. A 86 053424
[16] Zanghellini J, Kitzler M, Fabian C, Brabec T, Scrinzi A 2003 Laser Phys. 13 1064
[17] Kitzler M, Zanghellini J, Jungreuthmayer C, Smits M, Scrinzi, Brabec T 2004 Phys. Rev. A 70 041401
[18] Caillat J, Zanghellini J, Kitzler M, Koch O, Kreuzer W, Scrinzi A 2005 Phys. Rev. A 71 012712
[19] Kato T, Kono H 2004 Chem. Phys. Lett. 392 533
[20] Hochstuhl D, Bonitz M 2011 J. Chem. Phys. 134 084106
[21] Haxton D J, Lawler K V, McCurdy C W 2011 Phys. Rev. A 83 063416
[22] Liao C T, Li X, Haxton D J, Rescigno T N, Lucchese R R, McCurdy C W, Sandhu A 2017 Phys. Rev. A 95 043427
[23] Zhang B, Yuan J M, Zhao Z X 2015 Comput. Phys. Commun. 194 84
[24] Lamb W E, Schlicher R R, Scully M O 1987 Phys. Rev. A 36 2763
[25] Abramowitz M, Stegun I A 1972 Handbook of Mathmatical Functions (Washington:Dover) p752
[26] Rescigno T, McCurdy C 2011 Phys. Rev. A 62 032706
[27] Press W H, Teukolsky S A, Vetterling W T, Flannery B P 2007 Numerical Recipes (3rd Ed.) (New York:Cambridge University Press) pp179-193, 899-928
[28] Park T J, Light J C 1986 J. Chem. Phys. 85 5870
[29] Weinhold F, Landis C R 2001 Chem. Educ. Res. Pract. 2 91
[30] Zhang B, Yuan J M, Zhao Z X 2013 Phys. Rev. Lett. 111 163001
[31] Zhang B, Yuan J M, Zhao Z X 2012 Phys. Rev. A 85 033421
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[1] Xu G X, Li L M, Wang D M, Chen M B 2009 Quantum Chemistry:Fundamental Principle and Ab-initio Calculation Method (2nd Ed.) (Vol. 1) (Beijing:Science Press) pp869-874 (in Chinese)[徐光宪, 黎乐民, 王德民, 陈敏伯 2009 量子化学——基本原理和从头计算法(下) (第二版)(北京:科学出版社) 第869–874页]
[2] Becker W, Liu X J, Ho P J, Eberly J H 2012 Rev. Mod. Phys. 84 1011
[3] Zhao L, Zhang Q, Dong J W, L H, Xu H F 2016 Acta Phys. Sin. 65 223201 (in Chinese)[赵磊, 张琦, 董敬伟, 吕航, 徐海峰 2016 物理学报 65 223201]
[4] Jin F C, Wang B B 2016 Acta Phys. Sin. 65 224205 (in Chinese)[金发成, 王兵兵 2016 物理学报 65 224205]
[5] Hu S X 2013 Phys. Rev. Lett. 111 123003
[6] Ye D F, Liu X, Liu J 2008 Phys. Rev. Lett. 101 233003
[7] Brabec T, Krausz F 2000 Rev. Mod. Phys. 72 545
[8] Posthumus J H 2004 Rep. Progr. Phys. 67 623
[9] Xiao X R, Wang M X, Li M, Geng J W, Liu Y Q, Peng L Y 2016 Acta Phys. Sin. 65 220203 (in Chinese)[肖相如, 王慕雪, 黎敏, 耿基伟, 刘运全, 彭良友 2016 物理学报 65 220203]
[10] Zhang Z, Peng L Y, Xu M H, Starace A F, Morishita T, Gong Q H 2011 Phys. Rev. A 84 043409
[11] Guan X, Bartschat K, Schneider B I 2011 Phys. Rev. A 83 043403
[12] Stapelfeldt H 2003 Rev. Mod. Phys. 75 543
[13] Kulander K 1987 Phys. Rev. A 36 2726
[14] Marques M A L, Ullrich C A, Nogueira F, Rubio A, Burke K, Gross E K U 2006 Time-Dependent Density Functional Theory (Heidelberg, Berlin:Springer) pp1-13
[15] Hochstuhl D, Bonitz M 2012 Phys. Rev. A 86 053424
[16] Zanghellini J, Kitzler M, Fabian C, Brabec T, Scrinzi A 2003 Laser Phys. 13 1064
[17] Kitzler M, Zanghellini J, Jungreuthmayer C, Smits M, Scrinzi, Brabec T 2004 Phys. Rev. A 70 041401
[18] Caillat J, Zanghellini J, Kitzler M, Koch O, Kreuzer W, Scrinzi A 2005 Phys. Rev. A 71 012712
[19] Kato T, Kono H 2004 Chem. Phys. Lett. 392 533
[20] Hochstuhl D, Bonitz M 2011 J. Chem. Phys. 134 084106
[21] Haxton D J, Lawler K V, McCurdy C W 2011 Phys. Rev. A 83 063416
[22] Liao C T, Li X, Haxton D J, Rescigno T N, Lucchese R R, McCurdy C W, Sandhu A 2017 Phys. Rev. A 95 043427
[23] Zhang B, Yuan J M, Zhao Z X 2015 Comput. Phys. Commun. 194 84
[24] Lamb W E, Schlicher R R, Scully M O 1987 Phys. Rev. A 36 2763
[25] Abramowitz M, Stegun I A 1972 Handbook of Mathmatical Functions (Washington:Dover) p752
[26] Rescigno T, McCurdy C 2011 Phys. Rev. A 62 032706
[27] Press W H, Teukolsky S A, Vetterling W T, Flannery B P 2007 Numerical Recipes (3rd Ed.) (New York:Cambridge University Press) pp179-193, 899-928
[28] Park T J, Light J C 1986 J. Chem. Phys. 85 5870
[29] Weinhold F, Landis C R 2001 Chem. Educ. Res. Pract. 2 91
[30] Zhang B, Yuan J M, Zhao Z X 2013 Phys. Rev. Lett. 111 163001
[31] Zhang B, Yuan J M, Zhao Z X 2012 Phys. Rev. A 85 033421
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