Publications | Makri Group

166. R. Dani, S. Kundu and N. Makri, “Coherence maps and flow of excitation energy in the bacterial LH2 complex”, J. Phys. Chem. Lett. 14, 3835-3843 (2023).

165. N. Makri, “Topological aspects of system-bath Hamiltonians and a vector model for multisite systems coupled to local or common baths”, J. Chem. Phys. 158, 144107 (2023).

164. N. Makri, “Electronic frustration, Berry’s phase interference and slow dynamics in some tight-binding systems coupled to harmonic baths”, J. Phys. A 56, 144001 (2023).

163. S. Hammes-Schiffer, N. Makri and M. Rossi, “Simulating nuclear dynamics with quantum effects”, in Software for Electronic Structure Based Simulations in Chemistry and Materials, edited by Volker Blum and Theresa Windus (submitted).

162. R. Dani and N. Makri, “Time-Evolving Quantum Superpositions in Open Systems and the Rich Content of Coherence Maps”, J. Phys. Chem. B 126, 9361-9375 (2022).

161. S. Kundu, R. Dani and N. Makri, “Tight inner ring architecture and quantum motion of nuclei enable efficient energy transfer in bacterial light harvesting”, Science Advances 8, eadd0023 (2022).

160. R. Dani and N. Makri, “Quantum state-to-state rates for multistate processes from coherences”, J. Phys. Chem. Lett. 13, 8141-8149 (2022).

159. P. P. Roy, S. Kundu, N. Makri and G. R. Fleming, “Interference between Franck-Condon and Herzberg-Teller terms in the molecular spectra of metal-based tetrapyrrole derivatives”, J. Phys. Chem. Lett. 13, 7413-7419 (2022).

158. R. Dani and N. Makri, “Excitation energy transfer in bias-free dendrimers: Eigenstate structure, thermodynamics and quantum evolution”, J. Phys. Chem. C 126, 10309–10319 (2022).

157. S. Kundu, R. Dani and N. Makri, “B800-to-B850 relaxation of excitation energy in bacterial light harvesting: All-state, all-mode path integral simulations”, J. Chem. Phys. 157, 015101 (2022).

156. S. Kundu and N. Makri, “Small matrix quantum-classical path integral”, J. Phys. Chem. Lett. 13, 3492−3498 (2022).

155. S. Kundu, P. P. Roy, G. R. Fleming and N. Makri, “Franck-Condon and Herzberg-Teller signatures in molecular absorption and emission spectra”, J. Phys. Chem. B 126, 2899-2911 (2022).

154. P. Roy, S. Kundu, J. Valdiviezo, G. Bullard, James T. Fletcher, Rui Liu, S. J. Yang, P. Zhang, D. N. Beratan, M. J. Therien, N. Makri and G. R. Fleming, Synthetic control of exciton dynamics in bioinspired cofacial porphyrin dimers, J. Amer. Chem. Soc. 144, 6298-6310 (2022).

153. S. Kundu and N. Makri, “Intramolecular Vibrations in Excitation Energy Transfer: Insights from Real-Time Path Integral Calculations”, Annu. Rev. Phys. Chem. 73, 349-375 (2022).

152. N. Makri, “Small matrix path integral for driven dissipative dynamics”, J. Phys. Chem. A. 125, 10500 (2021).

151. R. Dani and N. Makri, “Quantum quench and coherent-incoherent dynamics of Ising chains interacting with dissipative baths”, J. Chem. Phys. 155, 234705 (2021).

150. S. Kundu and N. Makri, “Electronic-vibrational density evolution in a perylene bisimide dimer: mechanistic insights into excitation energy transfer”, Phys. Chem. Chem. Phys. 23, 15503-15514 (2021).

149. S. Kundu and N. Makri, “Time evolution of bath properties in spin-boson dynamics”, J. Phys. Chem. B 125, 8137–8151 (2021).

148. N. Makri, “Small matrix modular path integral: Iterative quantum dynamics in space and time”, Phys. Chem. Chem. Phys. 23, 12537-12540 (2021).

147. N. Makri, “Small matrix decomposition of Feynman path amplitudes”, J. Chem. Theory and Comput. 17, 3825-3829 (2021).

146. S. Kundu and N. Makri, “Origin of vibrational features in the excitation energy transfer dynamics of perylene bisimide J-aggregates”, J. Chem. Phys. 154, 114301 (2021).

145. A. Bose and N. Makri, “Quantum-classical path integral evaluation of reaction rates with a near-equilibrium flux formulation”, Int. J. Quantum Chem. e26618 (2021).

144. S. Kundu and N. Makri, “Exciton-vibration dynamics in J-aggregates of a perylene bisimide from real-time path integral calculations”, J. Phys. Chem. 125, 201–210 (2021).

143. S. Chatterjee and N. Makri, “Density matrix and purity evolution in dissipative two-level systems: II. Relaxation dynamics”, Phys. Chem. Chem. Phys. 23, 5125-5133 (2021).

142. S. Chatterjee and N. Makri, “Density matrix and purity evolution in dissipative two-level systems: I. Theory and path integral results for tunneling dynamics”, Phys. Chem. Chem. Phys. 23, 5113-5124 (2021).

141. M. Nava and N. Makri, “Quantum-classical path integral simulation of excess proton dynamics in a water dimer embedded in the gramicidin channel”, J. Chem. Theory and Comput. 17, 627-638 (2021).

140. N. Makri, “Small matrix path integral with extended memory”, J. Chem. Theory and Comput. 17, 1-6 (2021).

139. S. Kundu and N. Makri, “Real-time path integral simulation of exciton-vibration dynamics in light harvesting bacteriochlorophyll aggregates”, J. Phys. Chem. Letters 11, 8783-8789 (2020).

138 . S. Chatterjee and N. Makri, “Recovery of purity in dissipative tunneling dynamics”, J. Phys. Chem. Letters 11, 8592-8596 (2020).

137. S. Kundu and N. Makri, “Modular path integral for finite-temperature dynamics of extended systems with intramolecular vibrations”, J. Chem. Phys. 153, 044124 (2020).

136. S. Kundu and N. Makri, “Efficient matrix factorization of the modular path integral for extended systems”, Mol. Phys. 2020, DOI: 10.1080/00268976.2020.1797200

135. N. Makri, “Small matrix path integral for system-bath dynamics”, J. Chem. Theory and Comput. 16, 4038-4049 (2020).

134. A. Bose and N. Makri, “All-mode quantum-classical path integral simulation of bacteriochlorophyll dimer exciton-vibration dynamics”, J. Phys. Chem. B 124, 5028–5038 (2020).

133. N. Makri, “Small matrix disentanglement of the path integral: Overcoming the exponential tensor scaling with memory length”, J. Chem. Phys. (Commun.) 152, 041104 (2020).

132. S. Chatterjee and N. Makri, “Real-time path integral methods, quantum master equations, and classical vs. quantum memory”, J. Phys. Chem. B 123, 10470-10482 (2019).

131. S. Kundu and N. Makri, “Modular path integral for discrete systems with non-diagonal couplings”, J. Chem. Phys. 151, 074110 (2019).

130. F. Wang and N. Makri, “Quantum-classical path integral with a harmonic treatment of the back-reaction”, J. Chem. Phys. 150, 184102 (2019).

129. A. Bose and N. Makri, “Coherent state-based path integral methodology for computing the Wigner phase space distribution”, J. Phys. Chem. B 123, 4884-4894 (2019).

128. A. Bose and N. Makri, “Quasiclassical correlation functions from the Wigner density using the stability matrix”, J. Chem. Inform. Modeling 59, 2165-2174 (2019).

127. N. Makri, “Modular path integral methodology for real-time quantum dynamics”, J. Chem. Phys. 149, 204108 (2018).

126. A. Bose and N. Makri, “Wigner distribution by adiabatic switching in normal mode or Cartesian coordinates and molecular applications”, J. Chem. Theory and Comput. 14, 5446-5458 (2018).

125. N. Makri, “Modular path integral: Quantum dynamics via sequential necklace linking”, J. Chem. Phys. (Communication) 148, 101101 (2018).

124. A. Bose and N. Makri, “Non-equilibrium reactive flux: A unified framework for slow and fast reaction kinetics”, J. Chem. Phys. 147, 152723 (2017).

123. N. Makri, “Iterative blip-summed path integral for quantum dynamics in strongly dissipative environments”, J. Chem. Phys.146, 134101 (2017).

122. P. L. Walters, T. C. Allen and N. Makri, “Direct determination of harmonic bath parameters from molecular dynamics simulations”, J. Comput. Chem. 38, 110-115 (2017).

121. N. Makri, “Blip-summed quantum-classical path integral with cumulative memory”, Faraday Discuss. 195, 8192 (2016).

120. T. C. Allen, P. L. Walters and N. Makri, “Direct computation of influence functional coefficients from numerical correlation functions”, J. Chem. Theory and Comput. 12, 4169-4177 (2016).

119. P. L. Walters and N. Makri, “Iterative quantum-classical path integral with dynamically consistent state hopping”, J. Chem. Phys. 144, 044108 (2016).

118. P. L. Walters and N. Makri, “Quantum-classical path integral simulation of ferrocene-ferrocenium charge transfer in liquid hexane”, J. Phys. Chem. Lett. 6, 4959-4965 (2015).

117. A. Bose and N. Makri, “Evaluation of the Wigner distribution via classical adiabatic switching”, J. Chem. Phys. 143, 114114 (2015).

116. P. L. Walters, T. Banerjee and N. Makri, “On iterative path integral calculations for a system interacting with a shifted dissipative bath”, J. Chem. Phys. 143, 074112 (2015).

115. N. Makri, “Quantum-classical path integral: A rigorous approach to condensed-phase dynamics”, International Journal of Quantum Chemistry (Invited Perspective) 115, 1209-1214 (2015).

114. N. Makri, “Blip decomposition of the path integral: Exponential acceleration of real-time calculations on quantum dissipative systems”, J. Chem. Phys. 141, 134117 (2014). [Editor’s Choice for 2014.]

113. N. Makri, “Exploiting classical decoherence in quantum dissipative dynamics”, invited Frontiers article, Chem. Phys. Lett. 593, 93-103 (2014).

112. T. Banerjee and N. Makri, “Quantum-classical path integral with self-consistent solvent-driven propagators” (invited article for P. G. Wolynes Festschrift), J. Phys. Chem. B 117, 13357-66 (2013).

111. M. Sahrapour and N. Makri, “Tunneling, decoherence and entanglement of two qubits interacting with a dissipative bath”, J. Chem. Phys. 138, 114109 (2013).

110. R. Lambert and N. Makri, “Quantum-classical path integral: II. Numerical methodology” (invited article in special issue on Nonadiabatic Dynamics), J. Chem. Phys. 137, 22A553 (2012). [Editor’s Choice for 2012.]

109. R. Lambert and N. Makri, “Quantum-classical path integral: I. Classical memory and weak quantum nonlocality” (invited article in special issue on Nonadiabatic Dynamics), J. Chem. Phys. 137, 22A552 (2012). [Editor’s Choice for 2012.]

108. R. Lambert and N. Makri, “Memory path propagator matrix for long-time dissipative charge transport dynamics” (invited article for D. R. Herschbach Festschrift), Mol. Phys. 110, 1967-1975 (2012).

107. N. Makri, “Path integral renormalization for quantum dissipative dynamics with multiple timescales” (invited article for W. H. Miller Festschrift), Mol. Phys. 110, 1001-1007 (2012).

106. N. Makri, M. Head-Gordon, D. Chandler and W. T. Yang, “Quantum molecular dynamics: A Festschrift in honor of William H. Miller – Introduction”, Mol. Phys. 110, 493 (2012).

105. N. Makri, “Forward-backward semiclassical and quantum trajectory methods for time correlation functions”, Phys. Chem. Chem. Phys. 13, 14442-14452 (2011) (invited Perspective).

104. J. Chen and N. Makri, “Information-guided noise reduction in forward-backward semiclassical dynamics”, J. Chem. Theor. Comput. 7, 4-9 (2011).

103. C. Baltaretu and N. Makri, “Iterative Monte Carlo formulation of real-time correlation functions”, J. Chem. Phys. 133, 164103 (2010).

102. V. Jadhao and N. Makri, “Iterative Monte Carlo path integral with optimal grids from whole-necklace sampling”, J. Chem. Phys. 133, 114105 (2010).

101. V. Jadhao and N. Makri, “Iterative Monte Carlo with bead-adapted sampling for complex-time correlation functions”, J. Chem. Phys. 132, 104110 (2010).

100. J. Chen and N. Makri, “Low-temperature correlation functions via forward-backward quantum dynamics” (special issue in honor of Eli Pollak), Chem. Phys. 370, 15-19 (2010).

99. M. Sahrapour and N. Makri, “Nonlinear response functions in model dissipative systems”, J. Chem. Phys. 132, 134506 (2010).

98. J. Chen and N. Makri, “Time correlation functions via forward-backward quantum dynamics using Hamilton’s law of varying action”, J. Chem. Phys. 131, 124107 (2009).

97. E. Bukhman and N. Makri, “Mixed quantum and forward-backward semiclassical dynamics” (special issue in honor of R. Benny Gerber), J. Phys. Chem. 113, 7183-7188 (2009).

96. J. Kegerreis and N. Makri, “Direct Monte Carlo evaluation of real-time quantum correlation functions using single-step propagators”, Chem. Phys. Lett. 467, 430-434 (2009).

95. V. Jadhao and N. Makri, “Iterative Monte Carlo for quantum dynamics”, J. Chem. Phys. (Communication) 129, 161102 (2008).

94. J. Kegerreis, A. Nakayama and N. Makri, “Complex-time velocity autocorrelation functions for Lennard-Jones fluids with quantum pair-product propagators”, J. Chem. Phys. 128, 184509 (2008).

93. J. Chen and N. Makri, “Forward-backward semiclassical dynamics with single-bead coherent state density”, Mol. Phys. 106, 443-453 (2008).

92. N. Makri, “Equilibrium and dynamical path integral methods in bacterial photosynthesis”, in Biophysical Techniques in Photosynthesis, Volume II (Thijs J. Aartsma and Jörg Matysik, eds.), p. 465-485, Series: Advances in Photosynthesis and Respiration, Vol. 26, Springer, Dordrecht (2008).

91. E. Bukhman and N. Makri, “Forward-backward semiclassical dynamics with information-guided noise reduction for a molecule in solution” (special issue in honor of Thomas H. Dunning), J. Phys. Chem. A 111, 11320-11327 (2007).

90. J. Kegerreis and N. Makri, “Optimized Monte Carlo sampling in forward-backward semiclassical dynamics”, J. Comput. Chem. 28, 818-824 (2007).

89. A. Nakayama and N. Makri, “Symmetrized correlation functions for liquid para-hydrogen using complex-time pair-product propagators”, J. Chem. Phys. 125, 024503 (2006).

88. J. Liu, A. Nakayama and N. Makri, “Long-time behavior of quantized distributions in forward-backward semiclassical dynamics”, Mol. Phys. 104, 1267-1274 (2006).

87. J. Liu and N. Makri, “Symmetries and detailed balance in forward-backward semiclassical dynamics”, Chem. Phys. 322, 23-29 (2006).

86. A. Nakayama and N. Makri, “Simulation of dynamical properties of normal and superfluid helium”, Proc. Nat. Acad. Sci. U.S.A. 102, 4230-4234 (2005).

85. J. Liu and N. Makri, “Bohm’s formulation in imaginary time: Estimation of energy eigenvalues”, Mol. Phys. 103, 1083-1090 (2005).

84. N. Makri, “Information guided noise reduction for Monte Carlo integration of oscillatory functions”, Chem. Phys. Lett. 400, 446-452 (2004).

83. N. Makri, A. Nakayama and N. J. Wright, “Forward-backward semiclassical simulation of dynamical properties in liquids”, invited review, J. Theor. Comp. Chem. 3, 391-417 (2004).

82. K. Dong and N. Makri, “Quantum stochastic resonance in the strong field limit”, Phys. Rev. A 70, 042101 (2004).

81. A. Nakayama and N. Makri, “Forward-backward semiclassical dynamics for systems of indistinguishable particles”, Chem. Phys. 304, 147-158 (2004).

80. J. Liu and N. Makri, “Monte Carlo Bohmian dynamics from trajectory stability properties”, J. Phys. Chem. A 108, 5408-5416 (2004).

79. C. P. Lawrence, A. Nakayama, N. Makri and J. L. Skinner, “Quantum dynamics of simple fluids”, J. Chem. Phys. 120, 6621-6624 (2004).

78. N. J. Wright and N. Makri, “Phase space features and statistical aspects of forward-backward semiclassical dynamics”, J. Phys. Chem. B 108, 6816-6825 (2004).

77. N. Makri, “Forward-backward quantum dynamics for time correlation functions”, J. Phys. Chem. A 108, 806-812 (2004).

76. K. Dong and N. Makri, “Optimizing terahertz emission from double quantum wells”, Chem. Phys. 296, 273-279 (2004).

75. A. Nakayama and N. Makri, “Forward-backward semiclassical dynamics for quantum fluids using pair propagators: application to liquid para-hydrogen”, J. Chem. Phys. 119, 8592-8605 (2003).

74. N. J. Wright and N. Makri, “Forward-backward semiclassical dynamics for condensed phase time correlation functions”, J. Chem. Phys. 119, 1634-1642 (2003).

73. Y. Zhao and N. Makri, “Bohmian vs. semiclassical description of interference phenomena”, J. Chem. Phys. 119, 60-67 (2003).

72. N. Makri, “Monte Carlo evaluation of forward-backward semiclassical correlation functions with a quantized coherent state density”, J. Phys. Chem. B 106, 8390-8398 (2002).

71. N. Makri and W. H. Miller, “Coherent state semiclassical initial value representation for the Boltzmann operator in thermal correlation functions”, J. Chem. Phys. 116, 9207-9212 (2002).

70. Y. Zhao and N. Makri, “Quasiclassical dynamics methods from semiclassical approximations”, Chem. Phys. 280, 135-151 (2002).

69. J. Shao and N. Makri, “Iterative path integral formulation of equilibrium correlation functions for quantum dissipative systems”, J. Chem. Phys. 116, 507-514 (2002).

68. N. Makri and J. Shao, “Semiclassical time evolution in the forward-backward stationary phase limit”, in “Low-lying potential energy surfaces”, edited by M. R. Hoffman and K. G. Dyall, ACS Symposium Series, Volume 828 (2002).

67. J. Shao and N. Makri, “Iterative path integral calculation of quantum correlation functions for dissipative systems”, Chem. Phys. 268, 1-10 (2001).

66. N. Makri, “Forward-backward semiclassical dynamics”, in Fluctuating Paths and Fields, eds. W. Janke, A. Pelster, H.-J. Schmidt, and M. Bachmann, World Scientific, Singapore, 2001.

65. E. Jezek and N. Makri, “Finite temperature correlation functions via forward-backward semiclassical dynamics”, J. Phys. Chem. 105, 2851-2857 (2001).

64. N. Makri and G. C. Schatz, “Tribute to William H. Miller”, J. Phys. Chem. A 105, 2485-2486 (2001).

63. N. Makri, “Localization of dissipative tunneling systems driven by monochromatic light”, in Advances in Multiphoton Processes and Spectroscopy 14 (Quantum Control of Molecular Reaction Dynamics: Proceedings of the US-Japan Workshop, eds. R. J. Gordon and Y. Fujimura, World Scientific, Singapore), pp. 266-285, 2001.

62. J. Shao and N. Makri, “Forward-backward semiclassical dynamics in the interaction representation”, J. Chem. Phys. 113, 3681-3685 (2000).

61. N. Makri and J. Shao, “On the dissipative properties of coherent radiation”, Z. Physik. Chemie 214, 1187-1192 (2000).

60. N. Makri, “Iterative evaluation of the path integral for a system coupled to an anharmonic bath”, J. Chem. Phys. (Rapid Commun.) 111, 6164-6167 (1999).

59. O. Kühn and N. Makri, “Forward-backward semiclassical calculation of spectral lineshapes: I2 in a rare gas cluster”, J. Phys. Chem. 103, 9487-9493 (1999).

58. J. Shao and N. Makri, “Forward-backward semiclassical dynamics with linear scaling”, J. Phys. Chem. 103, 9479-9486 (1999).

57. J. Ray and N. Makri, “Short range coherence in the energy transfer of photosynthetic light harvesting systems”, J. Phys. Chem. 103, 9417-9422 (1999).

56. J. Shao and N. Makri, “Forward-backward semiclassical dynamics without prefactors”, J. Phys. Chem. (Letter) 103, 7753-7756 (1999).

55. N. Makri, “Time-dependent quantum methods for large systems”, Ann. Rev. Phys. Chem. 50, 167-191 (1999).

54. K. Thompson and N. Makri, “Rigorous forward-backward semiclassical formulation of many-body dynamics”, Phys. Rev. E 59, R4729-R4732 (1999).

53. K. Forsythe and N. Makri, “Dissipative tunneling in a bath of two-level systems”, Phys. Rev. B 60, 972-978 (1999).

52. J. Shao and N. Makri, “Influence functional from a bath of coupled time-dependent harmonic oscillators”, Phys. Rev. E 59, 269-274 (1999).

51. N. Makri, “The linear response approximation and its lowest order corrections: an influence functional approach”, J. Phys. Chem. (Letter) 103, 2823-2829 (1999).

50. K. Thompson and N. Makri, “Influence functionals with semiclassical propagators in combined forward-backward time”, J. Chem. Phys. 110, 1343-1353 (1999).

49. K. M. Forsythe and N. Makri, “Effects of frequency variation in modes orthogonal to the reaction path on condensed phase reaction rates”, J. Mol. Structure 466, 103-110 (1999).

48. N. Makri and K. Thompson, “Semiclassical influence functionals for quantum systems in anharmonic environments”, Chem. Phys. Lett. 291, 101-109 (1998).

47. N. Makri, “Dynamics of reduced density matrices: classical memory vs. quantum nonlocality”, J. Chem. Phys. 109, 2994-2998 (1998).

46. N. Makri, “Quantum dissipative dynamics: a numerically exact methodology”, J. Phys. Chem. A, invited Feature Article 102, 4414-4427 (1998).

45. N. Makri, “Tunneling in the condensed phase: barrier crossing and dynamical control”, in Classical and Quantum Dynamics in Condensed Phase Simulations, edited by B. J. Berne, G. Ciccotti and D. F. Coker, World Scientific, pp. 629-645 (1998).

44. G. Taft and N. Makri, “Effects of periodic driving on asymmetric two-level systems coupled to dissipative environments”, J. Phys. B 31, 209-226 (1998).

43. K. M. Forsythe and N. Makri, “Path integral study of hydrogen diffusion in crystalline silicon”, J. Chem. Phys. 108, 6819-6828 (1998); K. M. Forsythe and N. Makri, “Erratum on Path integral study of hydrogen diffusion in crystalline silicon”, J. Chem. Phys. 110, 6082 (1999).

42. E. Sim and N. Makri, “Path integral simulation of charge transfer dynamics in photosynthetic reaction centers”, J. Phys. Chem. B 101, 5446-5458 (1997).

41. N. Makri, “Path integral simulation of long-time dynamics in quantum dissipative systems”, in Functional Integration: Basics and Applications, edited by C. DeWitt-Morette, P. Cartier and A. Folacci, Plenum Press, pp. 193-211 (1997).

40. N. Makri, “Path integral methods”, in The Encyclopedia of Computational Chemistry, edited by P. v. R. Schleyer, N. L. Allinger, T. Clark, J. Gasteiger, P. A. Kollman, H. F. Schaefer III and P. R. Schreiner, John Wiley & Sons, Chichester, pp. 2021-2029 (1998).

39. N. Makri, “Stabilization of localized states in dissipative tunneling systems interacting with monochromatic fields”, J. Chem. Phys. 106, 2286-2297 (1997).

38. N. Makri and L. Wei, “Universal delocalization rate in driven dissipative two-level systems at high temperature”, Phys. Rev. E 55, 2475-2479 (1997).

37. E. Sim and N. Makri, “Filtered propagator functional for iterative dynamics of quantum dissipative systems”, Comp. Phys. Commun. 99, 335-354 (1997).

36. N. Makri, E. Sim, D. E. Makarov and M. Topaler, “Long-time quantum simulation of the primary charge separation in bacterial photosynthesis”, Proc. Natl. Acad. Sci. U.S.A. 93, 3926-3931 (1996).

35. E. Sim and N. Makri, “Tensor propagator with weight-selected paths for quantum dissipative dynamics with long-memory kernels”, Chem. Phys. Lett. 249, 224-230 (1996).

34. M. Topaler and N. Makri, “Path integral calculation of quantum nonadiabatic rates in model condensed phase reactions”, J. Phys. Chem. 100, 4430-4436 (1996).

33. D. E. Makarov and N. Makri, “Control of dissipative tunneling dynamics by continuous-wave electromagnetic fields: localization and large-amplitude coherent motion”, Phys. Rev. E 52, 5863-5872 (1995).

32. D. E. Makarov and N. Makri, “Stochastic resonance and nonlinear response in double quantum well structures”, Phys. Rev. B 52, R2257-2260 (1995).

31. N. Makri, “Numerical path integral techniques for long-time quantum dynamics of quantum dissipative systems”, J. Math. Phys. 36, 2430-2457 (1995).

30. E. Sim and N. Makri, “Time-dependent discrete variable representations for quantum wavepacket propagation”, J. Chem. Phys. 102, 5616-5625 (1995).

29. N. Makri and D. E. Makarov, “Tensor propagator for iterative quantum time evolution of reduced density matrices. II. Numerical methodology”, J. Chem. Phys. 102, 4611-4618 (1995).

28. N. Makri and D. E. Makarov, “Tensor propagator for iterative quantum time evolution of reduced density matrices. I. Theory”, J. Chem. Phys. 102, 4600-4610 (1995).

27. M. Topaler and N. Makri, “Quantum rates for a double well coupled to a dissipative bath: accurate path integral results and comparison with approximate theories”, J. Chem. Phys. 101, 7500-7519 (1994).

26. G. Ilk and N. Makri, “Real time path integral methods for a system coupled to an anharmonic bath”, J. Chem. Phys. 101, 6708-6716 (1994).

25. D. E. Makarov and N. Makri, “Path integrals for dissipative systems by tensor multiplication: condensed phase quantum dynamics for arbitrarily long time”, Chem. Phys. Lett. 221, 482-491 (1994).

24. D. E. Makarov and N. Makri, “Tunneling dynamics in dissipative curve crossing problems”, Phys. Rev. A 48, 3626-3635 (1993).

23. M. Topaler and N. Makri, “System-specific discrete variable representations for path integral calculations with quasi-adiabatic propagators”, Chem. Phys. Lett. 210, 448-457 (1993).

22. M. Topaler and N. Makri, “Quasi-adiabatic propagator path integral methods: exact quantum rate constants for condensed phase reactions”, Chem. Phys. Lett. 210, 285-293 (1993).

21. N. Makri, “Comment on ‘Monte Carlo evaluation of real-time Feynman path integrals for quantal many-body dynamics: distributed approximating functions and Gaussian sampling’”, J. Phys. Chem. 97, 8105-8106 (1993).

20. N. Makri, “On smooth Feynman propagators for real-time path integrals”, J. Phys. Chem. 97, 2417-2424 (1993).

19. M. Topaler and N. Makri, “Multidimensional path integral calculations with quasi-adiabatic propagators: quantum dynamics of vibrational relaxation in linear hydrocarbon chains”, J. Chem. Phys. 97, 9001-9015 (1992).

18. N. Makri, “Real-time path integrals with quasi-adiabatic propagators: quantum dynamics of a system coupled to a harmonic bath”, in Time-Dependent Quantum Molecular Dynamics, edited by J. Broeckhove and L. Lathouwers, Plenum Press, pp. 209-218 (1992).

17. N. Makri, “Improved Feynman propagators on a grid and nonadiabatic corrections within the path integral framework”, Chem. Phys. Lett. 193, 435-444 (1992).

16. N. Makri, “Time-dependent calculation of reaction rate constants: dynamical displacement operator treatment”, J. Phys. Chem. 95, 10413-10419 (1991).

15. N. Makri, “Accurate quantum mechanical calculation of thermally averaged reaction rate constants for polyatomic systems”, J. Chem. Phys. 94, 4949-4958 (1991).

14. N. Makri, “Time-dependent self-consistent field approximation with explicit two-body correlations”, Chem. Phys. Lett. 169, 541-548 (1990).

13. N. Makri, “Feynman path integration in quantum dynamics”, Comp. Phys. Commun. 63, 389-414 (1991).

12. N. Makri, “Effective non-oscillatory propagator for Feynman path integration in real time”, Chem. Phys. Lett. 159, 489-498 (1989).

11. R. A. Harris, C. J. Grayce, N. Makri, and W. H. Miller, “A corrected exponential power series expansion of the position matrix elements of the time evolution operator for a system in the presence of a vector potential”, J. Chem. Phys. 94, 4682-4683 (1991).

10. W. H. Miller, Y. T. Chang, and N. Makri, “Some new theoretical methods for treating reaction dynamics in polyatomic molecular systems”, in Computational Advances in Organic Chemistry: Molecular Structure and Reactivity, edited by C. Ogretir and I. G. Csizmadia, Kluwer Academic Publishers, pp. 289-302 (1991).

9. N. Makri and W. H. Miller, “A semiclassical tunneling model, for use in classical trajectory simulations”, J. Chem. Phys. 91, 4026-4036 (1989).

8. N. Makri and W. H. Miller, “Exponential power series expansion for the quantum time evolution operator”, J. Chem. Phys. 90, 904-911 (1989).

7. N. Makri and W. H. Miller, “Correct short time propagator for Feynman path integration by power series expansion in ”, Chem. Phys. Lett. 151, 1-8 (1988).

6. N. Makri and W. H. Miller, “Monte Carlo path integration for the real-time propagator”, J. Chem. Phys. 89, 2170-2177 (1988). error year