Correction to “DFT Modeling of Cross-Linked Polyethylene: Role of

Addition/Correction Cite This: J. Phys. Chem. A 2018, 122, 4591−4592

pubs.acs.org/JPCA

Correction to “DFT Modeling of Cross-Linked Polyethylene: Role of Gold Atoms and Dispersion Interactions” Martin Blaško,† Pavel Mach,‡ Andrej Antušek,§ and Miroslav Urban*,† †

Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University, Mlynská dolina, Ilkovičova 6, 841 04 Bratislava, Slovakia ‡ Department of Nuclear Physics and Biophysics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 84248 Bratislava, Slovakia § Advanced Technologies Research Institute, Faculty of Materials Science and Technology in Trnava, Slovak University of Technology in Bratislava, Bottova 25, 917 24 Trnava, Slovakia

J. Phys. Chem. A 2018, 122 (5), 1496−1503. DOI: 10.1021/acs.jpca.7b12232

B

singlet presented in Figure 4 is by 91 kJ/mol energetically more favorable to the triplet state with similar location of the two adjacent C−Au−C bonds.” The last sentence of the same paragraph should read “The absolute PBE0 + D3 energy of the triplet state with two remote gold atoms as presented in Figure 2A is by 133 kJ/mol higher than the energy of the closed shell PE15−Au2−PE15 complex with two adjacent gold atoms in Figure 4.” Section 3.3: The sentence in the second paragraph should read “For example, in the PE23−Au−PE23 cross-linked oligomer with 22 CH2−CH2 bonds it is 4.1 kJ/mol.” Conclusions: Two sentences in the first paragraph should read “With the PBE0 + D3 method our models for interchain interactions represented by closed shell oligomers containing 7−23 carbon atoms (PEn) lead to binding energies of 25−90 kJ/mol.” and “Already single Au atom cross-linking oligomers having 7−23 carbon atoms (PEn−Au−PEn) elevate BEs to 327−385 kJ/mol depending on the length of the oligomer chain.” The last sentence of this paragraph should read “This explains high binding energies for extended cross-linked oligomers, even though the contribution per single H2C··· CH2 bond (H3C···CH3 bonds for terminal oligomer groups) is small, 4.1 kJ/mol.”

y mistake, dispersion contributions to total binding energies in Tables 1−3 are systematically double counted. Therefore, total binding energies should be reduced accordingly. The red line in Figure 3 and the broken red line in Figure 6 are modified as well. Corrected tables and figures are attached below. Optimized energies of all polyethylene (PEn)−gold structures are presented correctly. General conclusions on the concerted role of gold atoms and dispersion interactions in models of gold cross-linked polyethylene remain valid. Binding energies mentioned in the original text should be changed as follows: In the Abstract, the numbers in the sentence starting with “Binding energies (BEs)...” should be “as high as 327−385 kJ/mol depending on the length of the oligomer chain.” The next to last sentence in the Abstract should read “BEs of pure saturated closed shell PEn−PEn oligomers are 25−90 kJ/mol.” Section 3.1: First paragraph, it should read “For 23 carbon atoms in each oligomer it is 296 kJ/mol, while with the Grimme dispersion-correction term D3 it is much larger, 385 kJ/mol.” In the same paragraph, it should read “This means that for our largest oligomer the dispersion contribution (90 kJ/mol including the geometry change) represents 23% of the total binding energy.” The last sentence in the second paragraph should read “...BEs are quite high, ranging from 106 to 163 kJ/mol for the smallest and with the largest PEn− Au−PEn cross-linked oligomers having 7 and 23 carbon atoms, respectively.” Section 3.2. Second paragraph, “The binding energy with respect to two PE15 triplet radical fragments and the two Au atoms (doublets) is 634 kJ/mol, i.e., 317 kJ/mol per single C− Au−C cross-link.” The next sentence should read “The BE with respect to the PE15 fragment (triplet) and the PE15−Au complex (singlet) is 191 kJ/mol.” The first sentence in the fourth paragraph should read “The binding energy of PE15− Au3−PE15 (quartet) with respect to two PE15 quartet radical fragments and three Au atoms (doublets) is 966 kJ/mol, i.e., 322 kJ/mol per single C−Au−C cross-link.” The three last sentences in nex to last paragraph of section 3.2 should read as follows: “With respect to the Au2 molecule and two closed shell alkenes having the C7C8 double bond the binding energy of PE15−Au2−PE15 is 64 kJ/mol. The corresponding Gibbs energy is −55 kJ/mol. The PE15−Au2−PE15 closed shell © 2018 American Chemical Society

Published: April 27, 2018 4591

DOI: 10.1021/acs.jpca.8b03343 J. Phys. Chem. A 2018, 122, 4591−4592

The Journal of Physical Chemistry A

Addition/Correction

Table 1. Binding Energies (BE, kJ/mol) for PEn−Au−PEn Cross-Linked Oligomersa with Respect to Fragments 2PEn* + Aub,c structures

PBE0

PBE0 + D3

PBE0 + D3(BJ)

PBE0 + D3 + 3body

PBE0 + D3(BJ) + 3body

PE7−Au−PE7 PE11−Au−PE11 PE15−Au−PE15 PE19−Au−PE19 PE23−Au−PE23

292.6 292.9 293.3 294.2 295.5

326.7(222.9) 340.1(223.1) 355.4(226.2) 370.2(221.5) 385.1(229.6)

329.5 341.8 355.5 369.0 378.4

325.5 337.5 351.8 365.6 374.7

328.6 339.8 352.7 365.4 374.1

a

Symbols PEn represent the number of carbon atoms in each oligomer used as a model for polyethylene. bPEn−Au−PEn, cross-linked complex, separated PEn* oligomer radicals, and Au are all doublets. cPBE0 energies correspond to structures optimized with the dispersion contribution neglected. D3 and alternative dispersion contributions (see section 2) are for structures optimized at the PBE0 D3 level. ΔG values at ambient conditions obtained with the PBE0 + D3 method are in parentheses.

Table 2. Binding Energies (BE, kJ/mol) for PEn−Au−PEn Cross-Linked Oligomers with Respect to Fragments PEnAu(singlet)−PEn*(doublet)a structures

PBE0

PBE0 + D3

PBE0 + D3(BJ)

PE7−Au−PE7 PE11−Au−PE11 PE15−Au−PE15 PE19−Au−PE19 PE23−Au−PE23

83.4 83.9 84.2 85.2 86.5

105.5(52.1) 118.4(51.6) 133.6(54.7) 148.4(50.7) 163.3(59.1)

106.3 118.0 131.6 145.0 156.5

PBE0 + D3 + 3body

PBE0 + D3(BJ) + 3body

104.6 116.0 130.2 144.0 155.5

105.5 116.1 128.9 141.5 152.2

a

Structures are optimized without (PBE0) and with the D3 contribution included. ΔG values at ambient conditions obtained with the PBE0 + D3 method are in parentheses.

Figure 6. D3 energies in PEn−Aux−PEn and in the crystal-like PEn− PEn closed shell structures at geometries optimized by the PBE0 + D3 method. The dotted line represents the D3 contribution to the binding energy in the PEn−Au−PEn cross-linked structure including the geometry change (see Table 1), with geometries optimized using PBE0 and PBE0 + D3 methods, respectively.

Table 3. PBE0 + D3 Binding Energies (kJ/mol) for Two Linear PEn−PEn Oligomers with Respect to Two PEn Fragments structures

PBE0+D3

PE7···PE7 PE11···PE11 PE15···PE15 PE19···PE19 PE23···PE23

24.8 41.3 57.8 74.4 90.1

Figure 3. Dependence of BEs of PEn−Au−PEn complexes on the number of carbon atoms in the oligomer. BEs are calculated with respect to fragments 2PEn + Au. Pure PBE0 results (blue line) and results with the D3 contribution (red line) are calculated at their optimized geometries.

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DOI: 10.1021/acs.jpca.8b03343 J. Phys. Chem. A 2018, 122, 4591−4592