Quantitative structure-property relationships prediction of some physico chemical properties of glycerol based solvents.

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1 Electronc Supplementary Informaton XXXXXXXX Electronc Supplementary Informaton for Quanttatve structure-property relatonshps predcton of some physco chemcal propertes of glycerol based solvents. José I. García,* a Héctor García-Marín, a José A. Mayoral, a,b and Pascual Pérez c a Insttuto de Síntess Químca y Catálss Homogénea, Facultad de Cencas, CSIC-Unv. de Zaragoza, Pedro Cerbuna, 12, E Zaragoza, Span. Tel: ; E-mal: jg@unzar.es. b Dept. Organc Chemstry, Facultad de Cencas, Unv. de Zaragoza, Pedro Cerbuna, 12, E Zaragoza, Span. E-mal: mayoral@unzar.es. c Dept. Physcal Chemstry, Facultad de Cencas, Unv. de Zaragoza, Pedro Cerbuna, 12, E Zaragoza, Span. E-mal: pascual@unzar.es. Content 1. Defnton of the topologcal parameters S2 2. Table S1, Topologcal parameters of 62 glycerol based solvents S5 3. Table S2, DARC/PELCO parameters of 62 glycerol based solvents S7 4. Table S3. Pearson bvarate correlatons between all the descrptors used n ths work S8 5. Fgure S1. Predcted vs. expermental values of E!!, vscosty, and bolng pont for the solvent test set usng MLR analyss wth topologcal parameters (equatons 2 4 n the man text). S9 6. Fgure S2. Predcted vs. expermental values of E!!, vscosty, and bolng pont for the selected solvent test set usng PLS analyss wth topologcal parameters. S9 7. Fgure S3. Predcted vs. expermental values of E!!, vscosty, and bolng pont for the selected solvent test set usng MLR analyss wth DARC/PELCO descrptors (equatons 5 7 n the text). S10 8. Fgure S4. Predcted vs. expermental values of E!!, vscosty, and bolng pont for the selected solvent test set usng MLR analyss wth mxed topologcal and DARC/PELCO descrptors (equatons 8 10 n the text). S10 9. Table S4. Comparson between MLR and PLS analyses wth DARC/PELCO descrptors for the three solvent propertes studed. S Table S5. Comparson between MLR and PLS analyses wth mxed topologcal and DARC/PELCO descrptors for the three solvent propertes studed. S Table S6. Summary of MLR and PLS results wth topologcal and DARC/PELCO descrptors for the three solvent propertes studed. S13 S1

2 Electronc Supplementary Informaton XXXXXXXX Defnton of the topologcal parameters Topologcal ndces are usually obtaned from two-dmensonal molecular structures (molecular graphs, G), mostly through the connectvty adjacency (A(G)) and topologcal dstance matrces (D(G)), and the vertex degree vector (δ(g)): A(G) δ(g) δ D(G) Topologcal ndces are calculated from dfferent nvarant features of the molecular graph, and contan nformaton about molecular sze, molecular shape, branchng, molecular flexblty, etc. The exact defnton of the ndces used n ths work are gven below. Balaban ndces (JX, JY):15, 23 Balaban ndex s defned as: M 1 J = M N + 2 a a s s where M s the number of bonds, N s the number of atoms n the molecule, and s s calculated as the sum of terms from a modfed topologcal dstance matrx. In ths modfed dstance matrx, each bond contrbutes wth 1/b to the total connectvty, wth b=1 for sngle bonds, b=2 for double bonds, b=3 for trple bonds, and b=1.5 for aromatc bonds:! s! = d!"!!! Correctons for heteroatoms have been ntroduced through contrbutons for the modfcaton of the electronegatvty (X) and the atomc rad (Y): where s the atomc number and G s the group number n the Perodc Table of the elements. From these correctons, the s!! values are defned as: s!! = X s! (for JX ndex) s!! = Y s! (for JY ndex) Wener ndex (W):16, 24 The Wener ndex s defned as the sum of the lengths of the shortest paths between all pars of vertces n the chemcal graph representng the non-hydrogen atoms n the molecule. It s easly computed from the topologcal dstance matrx: W = 1 2 Ths ndex s a measure of the centralty of the graph, and hence t s related wth the molecular compactness. Zagreb ndex:17 j X = 0,4196 0, , 1567 Y = 1,1191 0, , 0537! It s defned as the sum of squares of the dfference between the number of electrons partcpatng n covalent bonds and the number of hydrogen atoms bonded to the same atom. Ths s equvalent to the sum of the squares of the vertces degrees, δ :! d!" G G S2

3 Electronc Supplementary Informaton XXXXXXXX Randc and Ker & Hall connectvty ndces (χ):18 χ ndces were frst proposed by Randc25 from the vertces degrees, as: = 1 B, extended to all bonds n the molecule (B). δ δ j Ker and Hall extended the defnton by ncludng the number of edges of a gven sub-graph (h), and dfferent knds of sub-graphs (r):!! G =!!!!! where σ n s the number of sub-graph of length h and δ s the vertex degree. There are four knds of sub-graphs, known as path (lnear chans), cluster (branched chans), path/cluster, and chan (cycles), each one emphaszng a partcular aspect of the molecular connectvty. The n superndex refers to the number of bonds consdered to calculate the topologcal ndex. Thus, n=0 refers to ndvdual atoms, n=1 refers to drectly connected atoms, n=2 refers to three atoms connected through two consecutve bonds, and so on. n 1 1 n P( sub) = = ( δ δ j... δ n ) = 1 δ, and hence n n χ s Ch ( n)( sub) = P( sub) A further refnement10d, 18 can be ncluded to the χ ndcesby consderng the atom valences, thus allowng dstngushng the presence of heteroatoms n the structure. Ths s accomplshed by calculatng s corrected d value, usng the atomc number and the number of valence electrons of the vertex atoms: v v ( Z h) δ = v ( Z Z 1) Where Z v s the number of valence electrons, Z s the atomc number and h s the number of hydrogen atoms bonded to the vertex atom. The resultng valence-corrected ndces are named as χ v. Ker & Hall count ndces (SC): SC s the count of sub-graphs of a gven length present n the molecules. Thus, SC=0 s the number of atoms, SC=1, the number of chemcal bonds, SC=2, the number of par bonds, and so on. For longer sub-graphs, path, cluster, path/cluster and chan types can be also consdered. Ker shape ndces (κ n ): All the prededent topologcal ndces are heavly nfluenced by the sze of the molecular graph. Ker developed the κ ndces to best dscrmnate between dfferent shapes of the molecules. They are defned from sub-graphs of a gven length, takng nto account also the maxmum and mnmum connectvty of the molecule for the same length (a way to normalze the κ values, makng them ndependent of the molecular sze): m m Pmn Pmax κ n = K m P Where m s the length chosen of the sub-graph, m P the number of sub-graphs of length m contaned n the total graph, and m P max and m P mn s the maxmum and mnmum number possble of sub-graphs of length m that can contan the total graph. Some examples are gven below. κ 1, K =2: κ 2, K =2: κ 3, K =4: 2 P Zagreb = 1 P 2 δ = (σ h )!!!!!! ( ) 2 1 δ! 1 Pmn = N 1 1 N( N + 1) Pmax = 2 = number _ of _ edges 2 Pmn = N 2 ( N 1)( N 2) 2 Pmax = 2 = number _ of _ adjacent _ edges 2 S3

4 Electronc Supplementary Informaton XXXXXXXX Smlarly to the χ ndces, a modfcaton has been sugested for κ ndces to account for the presence of heteroatoms n the molecular graph. 14, 26 In ths modfcaton, both the covalent rad and the hybrdzatons are consdered. The!! ndces are defned as the κ n ones, but substtutng N by N+α, where a s defned as: Where r s the covalent radum of atom and r Csp 3 s taken as 0.77 Å (the covalent radus of a carbon atom wth sp 3 hybrdzaton). Molecular flexblty ndex (ϕ):14 3 P mn = N ( N 2) Pmax = ( N _ even) 4 ( N 1)( N 3) Pmax = ( N _ odd) 4 = tros _ of _ adjacent _ edges 3 3 P α = r r The startng hypothess to defne f s that an nfntely long lnear saturated hydrocarbon molecule (.e. all-sp 3 C C bonds) s nfntely flexble. Flexblty s reduced by the presence of a lmted number of atoms, rngs, branched chans, and the presence of atoms wth covalent rad shorter than that of C 3 sp : κ α κ α 1 2 ϕ = 3 Csp N 1 S4

5 Electronc Supplementary Informaton XXXXXXXX Table S1. Topologcal parameters of 62 glycerol based solvents. Code HBA HBD RB ϕ Bal JX Bal JY am am am W Z κ 1 κ 2 κ 3 SC p SC p SC p SC 3 p SC 0 c χ t t t t F F t03F F F03F F05F F07F t t t t χ 2 χ 3 χ p 3 χ cl 0 χ vm 1 χ vm 2 χ vm 3 vm χ p 3 vm χ cl S5

6 Electronc Supplementary Informaton XXXXXXXX t t t F t13F F F13F F23F F43F S6

7 Table S2. DARC/PELCO parameters of 62 glycerol based solvents. Code A1 A2 B1 B2 FB2 A11 A21 FA21 B11 B21 FB t t t t F F t03F F F03F F05F F07F t t t t t t t F t13F F F13F F23F F43F S7

8 Table S3. Pearson bvarate correlatons between all the descrptors used n ths work. A1 A2 B1 B2 BF2 C1 C2 CF2 D1 D2 DF2 HBA HBD RoB MFx BalJX BalJY W Z K1 K2 K3 SC0p SC1p SC2p SC3p SC3cl J0 J1 J2 J3p J3cl J0v J1v J2v J3pv J3clv A1 1 A B B BF C C CF D D DF HBA HBD RoB MFx BalJX BalJY W Z K K K SC0p SC1p SC2p SC3p SC3cl J J J J3p J3cl J0v J1v J2v J3pv J3clv Note that most topologcal parameters are heavly correlated to each other, whch ndcates that they recover essentally the same structural nformaton. Also, there are two pars of parameters fully dependent (r=1.000): C1/D1, κ 2 am /ϕ. S8

0,800 0,700 0,600 0,500 0,400 0,300 0,200 ETN 0,690 0,701 0,480 0,447 0,590 0,606 0,699 0,743 0,373 0,352 0,595 0,529 0,800% 0,700% 0,600% 0,500% 0,400% 0,300% 0,200% ETN$ 0,690% 0,680% 0,480% 0,472%

9 0,800 0,700 0,600 0,500 0,400 0,300 0,200 ETN 0,690 0,701 0,480 0,447 0,590 0,606 0,699 0,743 0,373 0,352 0,595 0,529 0,800% 0,700% 0,600% 0,500% 0,400% 0,300% 0,200% ETN$ 0,690% 0,680% 0,480% 0,472% 0,590% 0,618% 0,699% 0,666% 0,373% 0,337% % % 0,595% 0,518% 0,100 0,141 0,157 0,100% 0,141% 0,159% 0,000 40,0 35,0 30,0 25, F 5F05F 414t 4t13F 3F23F Dynamc vsc. (cp) 29,5 0,000% 40& 35& 30& 25& 200% 104% 303F% 5F05F% 414t% 4t13F% 3F23F% Dynamc$vsc.$(cP)$ % % 29,36& 20,0 15,0 10,0 5,0 0,0 35,1 6,9 13,5 1,0-2,5 2,1-2, F 113 4t13F 20& 15& 10& 5& 0&,5& 35,14& 6,9& 7,77& 1,03& 2,20& 2,14& 200& 303F& 113& 4t13F&,8,53& - 5,0,10& bolng pont (ºC) # 200# 150# Bolng$pont$(ºC)$ 231# 219# 195# 209# 173# 211# % % 182# 179# # 221# 208# 176# 204# 170# 234# 185# 171# 50 50# F 5F05F t 4t13F 3F23F 10 0# 200# 104# 303F# 5F05F# 113# 414t# 4t13F# 3F23F# Fgure S1. Predcted vs. expermental values of E!!, vscosty, and bolng pont for the selected solvent test set usng MLR analyss wth topologcal 5 parameters (equatons 2 4 n the man text). Fgure S2. Predcted vs. expermental values of E!!, vscosty, and bolng pont for the selected solvent test set usng PLS analyss wth topologcal parameters. 15 S9

0,900 0,800 0,700 0,600 0,500 0,400 0,300 0,200 ETN 0,690 0,661 0,480 0,497 0,590 0,609 0,699 0,795 0,373 0,290 0,595 0,506 0,800 0,700 0,600 0,500 0,400 0,300 0,200 ETN 0,690 0,670 0,480 0,474 0,590

(cp) 39,9 0,100 0,000 45,0 40,0 35,0 0,141 0,140 200 104 303F 5F05F 414t 4t13F 3F23F Dynamc vsc.

10 0,900 0,800 0,700 0,600 0,500 0,400 0,300 0,200 ETN 0,690 0,661 0,480 0,497 0,590 0,609 0,699 0,795 0,373 0,290 0,595 0,506 0,800 0,700 0,600 0,500 0,400 0,300 0,200 ETN 0,690 0,670 0,480 0,474 0,590 0,628 0,699 0,746 0,373 0,332 0,595 0,515 0,100 0,000 45,0 40,0 35,0 0,141 0, F 5F05F 414t 4t13F 3F23F Dynamc vsc. (cp) 39,9 0,100 0,000 45,0 40,0 35,0 0,141 0, F 5F05F 414t 4t13F 3F23F Dynamc vsc. (cp) 39,2 30,0 30,0 25,0 25,0 20,0 15,0 35,1 20,0 15,0 35,1 10,0 10,0 5,0 0, bolng pont (ºC) 6,9 5,6 1,0 2,6 2,1 2, F 113 4t13F ,0 0,0-5, bolng pont (ºC) 6,9 6,3 1,0 2,1-1, , F 113 4t13F F 5F05F t 4t13F 3F23F Fgure S3. Predcted vs. expermental values of E!!, vscosty, and bolng pont for the selected solvent test set usng MLR analyss wth DARC/PELCO descrptors (equatons 5 7 n the text) F 5F05F t 4t13F 3F23F Fgure S4. Predcted vs. expermental values of E!!, vscosty, and bolng pont for the selected solvent test set usng MLR analyss wth mxed topologcal and DARC/PELCO descrptors (equatons 8 10 n the text). 5 S10

11 Table S4. Comparson between MLR and PLS model coeffcents wth DARC/PELCO descrptors for the three solvent propertes studed. Descrptor N E T Dynamc Vscosty (cp) Bolng pont (ºC) MLR PLS a MLR PLS b MLR PLS c B A A B1 n.s n.s n.s. 5.0 B n.s BF n.s C1 n.s n.s C n.s CF D1 n.s n.s n.s D2 n.s n.s DF2 n.s n.s n.s. 3.0 N R σ a 4 latent varables. b 5 latent varables. c 6 latent varables. 5 Gven that C1 and D1 are lnearly dependent (see Table S3), ther behavour dffers n stepwse MLR and PLS analyses of the bolng pont response. In the former case, the varable enterng n the equaton takes the full value (33.6), whereas n the back-projecton of the PLS coeffcents nto the orgnal varables, each coeffcent takes half of the full value (15.3). Of course, the predctons wthn the solvent set used are therefore dentcal, gven that all structures for whch C1=1, have D1=1 too. Smlar, but not the same behavour s observed for other hghly correlated parameters, such as CF2 and DF2. 10 S11

12 Table S5. Comparson between MLR and PLS model coeffcents wth mxed topologcal and DARC/PELCO descrptors for the three solvent propertes studed. Descrptor N E T Dynamc Vscosty (cp) Bolng pont (ºC) MLR PLS a MLR PLS b MLR PLS c B A n.s A2 n.s B1 n.s n.s n.s B2 n.s n.s n.s BF n.s n.s C1 n.s n.s n.s C2 n.s n.s n.s CF2 n.s n.s n.s D1 n.s n.s n.s D2 n.s n.s n.s DF2 n.s n.s n.s HBA n.s n.s n.s HBD n.s n.s RB n.s n.s φ n.s n.s n.s Bal JX n.s n.s n.s Bal JY n.s n.s W n.s n.s n.s Z n.s n.s n.s κ 1 n.s n.s n.s κ 2 n.s n.s n.s κ 3 n.s n.s n.s SC 0 p n.s n.s n.s SC 1 p n.s n.s n.s SC 2 p n.s n.s n.s SC 3 p n.s n.s n.s SC 3 cl n.s n.s n.s χ n.s n.s χ n.s n.s n.s χ n.s n.s n.s χ p n.s n.s n.s χ cl n.s n.s n.s χ vm n.s χ vm n.s n.s n.s χ vm n.s n.s vm χ p n.s n.s n.s vm χ cl n.s n.s n.s N R σ a 6 latent varables. b 13 latent varables. c 9 latent varables. S12

13 Table S6. Summary of MLR and PLS results wth topologcal and DARC/PELCO descrptors for the three solvent propertes studed. Descrptor N E T Dynamc Vscosty (cp) Bolng pont (ºC) MLR PLS MLR MLR MLR PLS MLR MLR MLR PLS MLR MLR B A A B1 B BF C C CF D1 D DF2 HBA HBD RB φ Bal JX Bal JY W Z κ κ κ SC 0 p SC 1 p SC 2 p SC 3 p SC 3 cl χ χ χ χ p χ cl χ vm χ vm S13

14 2 χ vm vm χ p vm χ cl N R σ ,9 6.8 S14

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