ab initio path integral molecular dynamics: nuclear quantum effect Motoyuki Shiga CCSE, Japan Atomic Energy Agency, 6-9-3 Higashi-Ueno, Taito-ku, Tokyo 110-0015, Japan, Nuclear quantum effect such as zero point vibration or tunneling is important in molecular systems containing light atoms like hydrogen, and it is considered to have influence on the chemical and physical properties. In this presentation, first I would like to introduce the basic methodology of ab initio path integral molecular dynamics [1-4], in which both electrons and nuclei are treated quantum mechanically from first principles. Then, I will demonstrate some application studies on the quantum and thermal fluctuations of small water clusters using path integral simulations [5-13]. Particular focus here will be the geometrical isotope effect of hydrogen bonds. Finally, I will briefly comment on an efficient way for hybrid QM/MM path integral simulations [14], in order to deal with larger systems based on the ONIOM scheme [15]. [1] D. Marx and M. Parrinello, Z. Phys. B 95, 143 (1994). [2] D. Marx and M. Parrinello, J. Chem. Phys. 104, 4077 (1996). [3] M. Shiga, M. Tachikawa, and S. Miura, Chem. Phys. Lett. 332, 396 (2000). [4] M. Shiga, M. Tachikawa, and S. Miura, J. Chem. Phys. 115, 9149 (2001). [5] M. Shiga and T. Takayanagi, Chem. Phys. Lett. 378, 539 (2003). [6] M. Shiga and M. Tachikawa, Chem. Phys. Lett. 374, 229 (2003). [7] M. Tachikawa and M. Shiga, J. Chem. Phys. 121, 5985 (2004). [8] M. Tachikawa and M. Shiga, Chem. Phys. Lett. 407, 135 (2005). [9] W. Shinoda and M. Shiga, Phys. Rev. E 71, 041204 (2005). [10] M. Tachikawa and M. Shiga, J. Am. Chem. Soc. 127, 11908 (2005). [11] M. Shiga and W. Shinoda, J. Chem. Phys. 123, 134502 (2005). [12] M. Shiga and A. Nakayama, Chem. Phys. Lett. 451, 175 (2008). [13] K. Suzuki, M. Shiga, and M. Tachikawa, J. Chem. Phys. in press. [14] M. Shiga and M. Tachikawa, Mol. Simul. 33, 171 (2007). [15] K. Morokuma, Phil. Trans. R. Soc. London Ser. A 360, 1149 (2002).