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Fig.!1!Distance!convergence!with!respect!to!the!
number!of!beads!for!2nd!and!4th!order!Trotter!
expansions!at!300!K.!

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[F¯(H2O)]J

Haú\]%06,&7,89:;<=>¡ijZ

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H*

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O

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RIMP2! /aug"cc"pVDZ ef/2345wú 1 yZg]ÔÕ

Fig.!2!Schematic!illustration!of!F#!(H2O).

?>?@2¢nwH*YS 2 y¢n8^_`ij4o8^2¢nw­2öT\yùô5 F¯(H2O)?
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Table!1.!Average!values(Å)!and!these!statistical!errors!of!RFH*,!ROH*,!and!RFO!on!

!
!
!
!
!

quantum!H,!D,!and!classical!F#!(H2O).!
R FH*

R OH*

R FO

Classical!!F #!(H2O)

1.431 < 0.002

1.063 < 0.000

2.482 < 0.002

Quantum!F# !(H2O)

1.377 < 0.004

1.114 < 0.001

2.465 < 0.004

Quantum!F #!(D2O)

1.395 < 0.005

1.096 < 0.001

2.471 < 0.004

1.414

1.056

2.469

Equilibrium!
[1]!Edit!by!R.!R.!Dogonaze,!et!al,!The!chemical!physics!of!solvation!(Elsevir,!Amsterdam,!1985).![2]!W.!H.!Robertson,!et!al,!Science,!
299,!1367(2003).![3]!P.!Ayotte,!et!al,!J.!Chem.!Phys.,!110,!7129(1999).![4]!P.!Ayotte,!et!al,!J.!Phys.!Chem.!A,!103,!10665(1999).![5]!G.!M.!
Chaban,!et!al,!J.!Phys.!Chem.!A,!107,!4952!(2003).![6]!S.!S.!Xantheas,!et!al,!J.!Phys.!Chem.,!98,!13489!(1994).![7]!K.!Suzuki,!et!al,!J.!Chem.!
Phys.,!129,!144310!(2008).![8]!M.!Takahashi,!et!al.!J.!Phys.!Soc.!Jpn.,!53,!3765(1984).! !