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# Errata

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## Scientific publications Philippe H**ü**nenberger: typos and minor errors

This page provides a list of typos and minor errors discovered in my publications after printing (please, don't hesitate to contact me if you find others); two articles, [17] and [55], were affected by more significant errors, justifying the publication of an erratum.

The numbering refers to my **publication list**

[14] Hünenberger & McCammon, J. Chem. Phys. **110** 1856 (1999)

- Page 1868, Eq(A11): δ
_{j,I}should be replaced by δ_{j,J}and δ_{k,I}by δ_{k,K} - Page 1868, Eq(A11) is incorrect as written: the 6 terms in lines 2-4 of Eq(A6) should be added to the left-hand-side of this equation

[17] Baker *et al.*, J. Chem. Phys. **110** 10679 (1999)

- Page 10688, Eq(66): the sign of the last term in the right-hand side should be minus instead of plus, see our book p 79 [Eq(3.42) and following lines] where this error was reported
- See also Erratum: J. Chem. Phys.
**113**2510 (2000)

[18] Hünenberger, In "Simulation and theory of electrostatic interactions in solution..." pp 17-83 (1999)

- Page 27, Figure 4: The labels of the LΨ and LΨ
_{η}curves should be swapped, i.e. LΨ_{η}is the solid line and LΨ the short-dashed line - Page 34, 9 lines below header "Shaping functions": -2.837927 should be replaced by -2.837297

[22] Heinz *et al.*, J. Chem. Phys. **115** 1125 (2001)

- Page 1127, 4 lines below Eq(14): p~
_{α}(nΔN) should read p~_{α}(nΔM)

[25] Börjesson & Hünenberger, J. Chem. Phys. **114** 9706 (2001)

- Page 9708, Eq(6): in the right-hand side of the equation, the sum over the 2
^{N}vectors**l**(all possible N-dimensional vectors with components equal to 0 or 1) should actually involve terms that are products from i=1 to N of the indicated quantity - Page 9708, Eq(6): this equation is also somewhat clumsy, because it implies the convention 0
^{0}=1 (this case can occur when λ_{i}=0 or λ_{i}=1) - Page 9708, Eq(6): finally, the Hamiltonian H in the right-hand side should probably rather be called H
_{phy}, and corresponds to physical (0 or 1) protonation states (otherwise, it seems that H_{tot}is used in this equation to define itself) - This article has been criticised by Baptista, J. Chem. Phys.
**116**7766 (2002); we think at present that the criticism is justified, and agree that the proposed constant-pH method is empirical in nature (mean-field approximation), rather than formally rigorous, as initially thought

[37] Pereira *et al.*, Biophys. J. **86** 2273 (2004)

- Table 1, 3 entries at 475K: the reported values for D
_{xy}and D_{z}should be divided by 10, see [56] p 15575 (Table 1, footnote a) where this error was reported - Figure 4, graph legend: CH
_{2}Glycerol should read CH_{1}Glycerol

[41] Hünenberger, Adv. Polymer. Sci. **173** 105 (2005)

- Table 1, entry μPR: the name of the ensemble should be "grand-isoenthalpic-isobaric" and not "grand-isothermal-isobaric"
- Page 114, Eq(12): the quantity summed over i in the right-hand side should read m
_{i}[(**r**_{i}-**r**_{CM})^{2}- (__1__**r**_{i}-**r**_{CM}) ⊗(**r**_{i}-**r**_{CM})] instead of m_{i}(**r**_{i}-**r**_{CM}) ⊗(**r**_{i}-**r**_{CM}) - Page 128, Eq(56): the prefactor in the right-hand-side should be -1/2 instead of 1/2
- Page 128, Eq(57): the prefactor of the second term in the right-hand-side should be +1/2 instead of -1/2
- Page 143, Eq(113), line 3: left-hand-side, in -∂ρ/∂γ⋅γ, the second γ should be γ-dot (dot overscript)

[47] Heinz & Hünenberger, J. Chem. Phys. **123** 034107 (2005)

- Page 4, Eq(9): the second sum should involve index j instead of i
- Page 5, 6 lines below Eq(25): -2.837927 should be replaced by -2.837297
- Page 7, Eq(41): the second sum should involve index j instead of i
- Page 9, Eq(65): the quantity k
^{3}R_{RF}in the denominator of one of the fractions (second line) should actually be k^{3}R^{3}_{RF} - Page 9, Eq(65): the last condition k≠0 (bottom of the second line) should actually be k=0
- Page 18, Eq(C1): e
^{-κ2}/4 should be replaced by e^{-κ2/4}

[49] Christen *et al.*, J. Comput. Chem. **26** 1719 (2005)

- Table 7, entry p=3: w
_{p}(ξ) should read 3/4-ξ^{2}instead of -(3/4)(4ξ^{2}-1)

[50] Kastenholz & Hünenberger, J. Chem. Phys. **124** 124106 (2006)

- Page 8, Point (1): the estimated value of ΔΦ
_{ODL}for liquid argon at 87K based on the Slater-type analysis should be -411 kJ mol^{-1}*e*^{-1}(-4.26 V) instead of -463 kJ mol^{-1}*e*^{-1}(-4.80 V), see below - Supplementary Material, Eq(S2.2): η should be 21.6 instead of 24.3 nm
^{-3}, and ΔΦ^{QM}_{ODL}should be -411 instead of -463 kJ mol^{-1}*e*^{-1}, the reason is that the molar mass of argon was erroneously set to 35.45 instead of 39.948 g mol^{-1}, see our book p 283 [Eq(4.342) and following lines], 284 [Eq(4.347) and following lines] and 285, where the correct results are reported

[51] Kastenholz & Hünenberger, J. Chem. Phys. **124** 224501 (2006)

- Table III, entries LS/2048, LA/2048 and LV/2048: box edge (3
^{rd}column) should be 3.94 instead of 3.13 nm - Page 7, 4 lines below Eq(39): one could expect the correction term to be proportional to (1-ε
_{S}^{-1}), and not (1-ε_{S})^{-1}as written; however, even in this altered form, the statement is not correct, see [85] p 5 [comment just below Eq(15)] or our book p 504 (comment just below Table 6.2), where the statement is ammended

[55] Pereira *et al.*, Biophys. J. **90** 4337 (2006)

- Figure 1, drawing for Nigerose (N): the arrow marked 49.5% should point in the opposite direction, see Table 1 where the H-bond considered is (correctly) reported in the direction HO
_{4}'→O_{2} - Table 1, caption, lines 1-2: the ω' values should read gg -60° and gt +60°, see [79] pp 1784-1786 and 1790 as well as [84] pp 1002-1004 for precise (and correct) definitions
- See also Erratum: Biophys. J.
**93**706 (2007) - The erratum also contains a serious mistake in its Table 1: the entries ΔS
_{cl}^{ah}and ΔS_{cl}^{pc}should be multiplied by 8.314, and the entries S^{ctd}and -TΔS^{ctd}recalculated accordingly, see [79] p 1796 where this error was reported

[57] Baron *et al.*, Trends Phys. Chem. **11** 87 (2006)

- Page 118, Eq(C5): the left-hand-side of this equation should read ln κ
_{1}^{o}instead of κ_{1}^{o} - Page 118, Eq(C6): the left-hand-side of this equation should read ln κ
_{2}^{o}instead of κ_{2}^{o}

[66] Perić *et al.*, **34** 421 (2008)

- Abstract, line 3: abreviation for poly-α(1→4)-L-guluronate should read pGulU instead of pGlcU

[65] Kräutler & Hünenberger, Mol. Simul. **34** 491 (2008)

- Figure 4: the radial distribution functions are incorrectly normalized, probably to unity (three bottom panels) or half-unity (top panel) instead of the box volume V
_{box}(*i.e.*the integral of 4πr^{2}g(r) is one or one-half instead of V_{box}); the reported g(r) have thus units of nm^{-3}and must be scaled by V_{box}(three bottom panels) or 2V_{box}(top panel) with V_{box}= 287.5 (CU box) or 228.3 (TO box) nm^{3}to obtain properly normalized (unitless) radial distribution functions.

[81] Horta *et al.*, J. Chem. Theory Comput. **6** 2488 (2010)

- Page 2491, 15 lines below Table 1: a value of 4.575·10
^{-4}(kJ·mol^{-1}·nm^{-3})^{-1}was used for the simulations, but it is not the value appropriate for pure water, which would be 7.505·10^{-4}(kJ·mol^{-1}·nm^{-3})^{-1}based on a compressibility of 4.52·10^{-5}bar^{-1}at 25°C; the value used is the approximate value suggested in the GROMOS96 manual for a 1:1 protein-water mixture - Page 2493, Table 3: the numbers reported in this table and discussed in the text for N
_{LL}^{intra}and N_{WW}are actually not the average numbers of intralayer lipid-lipid and water-water H-bonds, respectively, but twice these numbers; given this doubling, the scaling of N_{LL}^{intra}by the number of lipids in the system provides the average number of lipids H-bonded to a given lipid within a leaflet, and the discussion on page 2493 (right column, second paragraph) is correct; note that unlike N_{LL}^{intra}, N_{LL}^{inter}is not doubled,*i.e.*it is the average number of interlayer lipid-lipid H-bonds; this is a nomenclature issue and not a mistake, see [99] for a more consistent formulation - Page 2493, Table 3: in addition to the previous nomenclature issue, the numbers reported in this table for N
_{LL}^{intra}(*i.e.*twice the average number of intralayer lipid-lipid H-bonds) are affected by a small calculation mistake; the correct values can be obtained by subtracting N_{LL}^{inter}from these numbers; the error is essentially negligible (with the possible exception of the three last entries at quarter hydration) and does not affect the main conclusions of the discussion on page 2493 (right column, second paragraph) - Page 2497, Figure 5, points at
*n*=2: the values for these points are affected by a small calculation error and are too low (this problem also affects [99], Figure 3), see [104] (caption of Figure 9) and [105] (caption of Figure 8) where the error was reported and correct values for these points can be found

[82] Hansen *et al.*, J. Chem. Theory Comput. **6** 2596 (2010)

- Page 2617, 6 lines below Eq (A.8): k
_{LE}is equal to (2πσ)^{NLE/2}c_{LE}and not (2πσ)^{NLE/2cLE}

[83] Hansen & Hünenberger, J. Chem. Theory Comput. **6** 2622 (2010)

- Page 2627, 4 lines above Eq (5): W
_{l}should be referred to as a "half" width instead of a "double" width,*i.e.*the width of the "tube" defined by the flat-bottom region of the transverse biasing potential is 2W_{l} - Page 2631, Eq(27): this equation as well as the following descriptive lines are formally incorrect (although the calculations were performed correctly); <X(
**r**)>_{Q(r)∈S}should be replaced by <X(**r**)θ(**r**)> where θ(**r**) is one if**Q**(**r**)∈*S*and zero otherwise, and the averaging is performed over the entire biased ensemble; since C_{G}can be chosen arbitrarily, this is equivalent to an integral (and not an average) over the region for which**Q**(**r**)∈*S*

[84] Hansen & Hünenberger, J. Comput. Chem. **32** 998 (2011)

- Table 2, last line, improper dihedrals for β-Glc: C
_{2}-C_{1}-O_{1}-C_{2}must be changed to C_{2}-C_{3}-C_{1}-O_{2}, and C_{5}-O_{5}-C_{6}-C_{4}to C_{5}-C_{4}-O_{5}-C_{6} - Table 3, entry C6: 45A4/53A6 as well as 56A
_{CARBO}atom types are incorrect and should both be CH_{2} - Tables 3 and 4: the atom type HO actually does not exist in GROMOS - in the force-field files, it is listed simply as H
- Table 6, entry T1, dihedrals for β-Glc: O
_{5}-C_{5}-C_{6}-O_{6}should rather be defined as C_{4}-C_{5}-C_{6}-O_{6}to follow the the IUPAC definition of ω; this does not matter much in practice since T1 is a 3-fold term (the definition C_{4}-C_{5}-C_{6}-O_{6}is adopted in the current GROMOS force-field files) - Table 6, entry T3, dihedrals for β-Glc: C
_{5}-C_{4}-O_{4}-H_{4}should rather be defined as C_{3}-C_{4}-O_{4}-H_{4}to follow the systematism of the other dihedrals and the IUPAC definition of χ_{4}; this does not matter much in practice since T3 is a 3-fold term (the definition C_{3}-C_{4}-O_{4}-H_{4}is adopted in the current GROMOS force-field files) - Table 8, Gal ω-rotamers, entry for 45A4(β) from Ref 73: the populations should be 34, 41 and 25 (instead of 34, 41 and 35)

[85] Reif & Hünenberger, J. Chem. Phys. **134** 144103 (2011)

- Page 7, Eq. 32: This equation is formally not correct, considering that q
_{I}=0 in the situation considered here. One should write instead: χ^{ion}= Φ_{o}^{raw}+ [2/(N_{A}q_{I}) ΔG_{B}^{LS}]^{*}+ [1/(N_{A}q_{I}) ΔG_{C1}^{LS}]^{*}, where the "*" superscript indicates that the quantity is simplified assuming q_{I}≠0 and subsequently evaluated at q_{I}=0. From Eq. 18, the second term in the right-hand-side is zero. From Eq. 24, the third term in the right-hand-side is -N_{A}[1-4πR_{I}^{3}/(3 L^{3})]ξ'_{S} - Page 7, Eq. 33: In contrast to the preceding one, this equation considers q
_{I}to be the full ionic charge. Following from the previous comment, the second term in the parenthesis of the right-hand-side should be zero,*i.e.*the equation is incorrect and should read ΔG_{C1}^{LS}= 4πR_{I}^{3}/(3 L^{3}) (N_{A}q^{I}Φ_{o}^{raw}+ΔG_{C1}^{LS}). Note that the error affects the article but not the calculation results, which actually relied on the correct equation

[86] Reif & Hünenberger, J. Chem. Phys. **134** 144104 (2011)

- Figure 2: a strange "20p0" artifact (in black) has appeared in the middle of the figure upon printing (should be ignored)

[88] Horta *et al.*, J. Chem. Theory Comput. **7** 10161 (2011)

- Table 4, entry ether/OE: charge in 53A6
_{variant}should be -0.420 instead of 0.420 - Table 4, entry aldehyde/O: charge in 53A6
_{OXY}should be -0.475 instead of 0.475 - Table 7, entry 53A6
_{OXY}for DXE: hydration free energy ΔG_{wat}should be -16.1 +/- 1.8 kJ/mol instead of -18.5 kJ/mol +/- 1.8 (the reported value was mistakenly calculated using a slightly modified OCCO torsional-energy term), see [98] Table 6 where this error was reported (this value is also recalculated therein using a slightly different calculation protocol but the normal OCCO torsional-energy term of 53A6_{OXY}, resulting in -14.7 +/- 0.1 kJ/mol) - Page 1023, left column, line 23: a value of 4.575·10
^{-4}(kJ·mol^{-1}·nm^{-3})^{-1}was used for the simulations in water, but it is not the value appropriate for pure water, which would be 7.505·10^{-4}(kJ·mol^{-1}·nm^{-3})^{-1}, see corresponding note under [81]; the error incurred is probably negligible, considering that this parameter is combined with the arbitrary barostat coupling time, which has itself a very limited influence on the thermodynamic properties of the system

[90] Choutko *et al.*, Chem. Phys. Chem. **12** 3214 (2012)

- Page 3219, left column, lines 29-30: "a slight excess of W
_{2}^{L}over W^{L}water units is observed at the wall" should be "a slight excess of W^{L}over W_{2}^{L}water units is observed at the wall"

[93] Kunz *et al.*, J. Comput. Chem. **33** 340 (2012)

- Page 342, Eq. 18: the first summation over index i should be deleted, and the second summation replaced by a summation over j≠i instead of j>i.

[98] Fuchs *et al.*, J. Chem. Theory Comput. **8** 3943 (2012)

- Table 7, entry rms for 53A6
_{OXY}rec: "[0.03]" should read "[0.04]" (rounding error). - Table 7, entry rms for 53A6
_{OXY+D}: "[0.97]" should read "[0.03]".

[99] Laner *et al.*, Mol. Simul. **39** 563 (2013)

- Page 579, left column, line 11: in terms of entropy, the factor is about 2.7 (122.2/46) and not 3.8, see [Laner,KIN] p XXX where this error was reported (a value of 2.5 is actually proposed therein based on more extensive simulations)
- Page 576, Figure 4, points at
*n*=11: the values for these points are affected by a small calculation error and are too low (this problem also affects [81], Figure 5), see [104] (caption of Figure 9) and [105] (caption of Figure 8) where the error was reported and correct values for these points can be found

[101] Wang *et al.*, Eur. Biophys. J. **42** 521 (2013)

- Page 534, left column, line 40: "it contributes to affinity and not to specificity, and is thus a steering force" should read "it contributes to specificity and not to affinity, and is thus a steering force"

[102] Rocklin *et al.*, J. Chem. Phys. **139** 184103 (2013)

- Page 17, caption Table II, and p 23, caption Table IV : the value of γ
_{S}should read 0.00764*e*nm^{2}(2*0.417*0.09572^{2}for TIP3P water; instead of 0.0764 as written); this is just a typo, all calculations were performed with the correct value.

[BOOK]

- see specific web page for the book erratum