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Ab initio stability study of the geometric isomerism of acyclic imines and O-protonated carbonyl compounds
Journal of Molecular Structure (Theochem), 276 (1992) 187-208 Elsevier Science Publishers B.V., Amsterdam
187
Ab initio stability study of the geometric isomerism of acyclic imines and 0-protonated carbonyl compounds. Part II. Model compounds for additive schemes of anti-syn conversion energies: imino- and 0-protonated derivatives of propynal, butynone and butynonal T.-K. Ha and H.H. Gunthard Physical
Chemistry Laboratory,
ETH Zentrum,
CH-8092 Zurich (Switzerland)
(Received 28 January 1992)
Abstract The problem of decomposing the conversion energies of the geometrical isomers of acyclic isoelectronic imines and 0-protonated carbonyl compounds into intuitive contributions associated with the repulsive intramolecular interactions of imino hydrogen atoms (hydroxyl hydrogen atoms) with hydrogen atoms bound to neighbouring carbon atoms is considered. The investigation was based on quantum chemical computations at the HartreeFock level with the 6-31G* and 6-31G** basis sets for 14 acyclic imines, 14 0-protonated carbonyl species, 10 model imines and 10 model 0-protonated systems. Definitions of specific (1,4 and 1,5) hydrogen contributions (E,, and E,,) and rules for decomposing the conversion energies into additive contributions are proposed. Application of the procedure to the geometrical isomers of model compounds (imines HCC*CH:NH, HCC.C(:NH).CH:CH,, HC!C.C(:NH)CHO, HC:C*C(:NH)CH:NH, HC:C.C(:NH)CH,, and 0-protonated species HCiC*CH:Op, HCiC.C(:Op)CH:CH,, HCC.C(:Op)CH, HCIC.C(:Op)CH:O and HCC.C(:Op)CH:NH) (p denotes a proton) gives zeroth-order estimates of particular contributions. These estimates were used to determine a set of specific contributions, which in turn permit one to reconstruct the conversion energies of the geometrical isomers of acyclic isoelectronic imines and 0-protonated carbonyl compounds by using a simple additive scheme. The conversion energies were reproduced to within 0.2-0.3 kcal mall’. The contribution terms are expected to be fairly generally applicable.
INTRODUCTION
In a recent paper a quantum chemical investigation (Hartree-Fock
(HF)
6-31G* or second-order Moller-Plesset (MP2) 6-31G**//6-31G** level) of the Correspondence to: H.H. Gunthard, Physical Chemistry Laboratory, ETH Zentrum, CH8992 Zurich, Switzerland.
0166-1280/92/$05.00 0 1992 Elsevier Science Publishers
B.V. All rights reserved.
188
T.-K. Ha, H.H. GunthardlJ.
Mol. Struct. (Theo&em)
276 (1992) 187-208
correlation between the geometrical isomerism of simple acyclic isoelectronic imines and 0-protonated carbonyl compounds of the structural types (X, Y = H or CH,; Z = CH,, 0 or NH; p denotes a proton)
hP,
lH/
iCl
ri Cl
X
Y /\ / X
NY
/ \
c2
c2
(1)
II 2
II z
0-protonated types p0 anti ClC2 p0 syn ClC2
Imine types HN anti ClC2 HN syn ClC2
and the total electronic energy and internal structural parameters (bond length and bond angles) has been reported [l]. Of the results obtained in that study, the following should be briefly ment’ ,M_e;r;)m~e a-nzb;;; isomers with Z = :CH, or of the type HN=C\ < 0.5 kcalmolll than HN syn isomers; (ii) HN anti ClC2 isomers with Z = :0 or :NH are more stable by > 2 kcal mall’; (iii) conversion from anti to syn isomers implies a narrowing of L NC,X( L OC,X) and a widening of L NC, C, ( L OC, C,) by 2 5’; (iv) L HNC,, L pOC, and L XC, C, are nearly independent of the geometrical isomerism of the imino (0-protonated carbonyl) group; (v) anti-syn conversion causes the d(l3-N) (d(p0)) bond length to increase slightly (2mA); d(Cl-C2) increases by 4-5 mA and d(X(C,)-C,) decreases by approximately 4mA (X = H or CH,). Furthermore, the data obtained on these imines and 0-protonated carbonyl compounds suggest that the anti-syn conversion energies, e.g. of the process H \
/” iiy
X/ anti
y
ii
+ X’
y 71’
vn
are composed of additive contributions of the type El4(H . . . X> or El5{H . . . Y}, i.e. of 1,4 or 1,5 l3-H interactions of Urey-Bradley type. However, from the data derived in that study it was not possible to arrive at approximate numerical values for such contributions. The derivation of energy increments in order to estimate conversion energies seems to be of some general interest. A typical case of interest is the relatively large set of geometrical isomers of the various tautomers of the nucleic acid bases, where experimental determination of the equilibria of all tautomeric forms including
the geometrical isomerism of hydroxyl and imino groups might be difficult. Although quantum chemical calculation of the relative stabilities of such a set of isomers is complicated by the intricacies of basis-set dependence, it might, on grounds of experience, be expected that the basis-set dependence of the conversion energies of geometrical isomers will remain tolerable, provided these are computed at a sufficiently high level. Analogously, the changes in the internal structural parameters associated with geometrical isomer conversion have been found to depend only slightly on the basis sets 3-21G to 63IG** (see ref. 1). In this paper we first present quantum chemical optimized energy and optimized structural data of a set of model compounds. The calculations were done using HF/6-31G” and HF/6-31G** basis sets, The model compounds (essentially derivatives of propynoic acid HC : C * COOH) 0
were chosen such that the conversion energies of the geometrical isomers would serve as reference and additional energy data for determining a system of additive contributions to the electronic conversion energies of the imines and 0-protonated carbonyl compounds studied in ref. 1. Schemes 1 and 2 show the schematic formulae of the molecules chosen. The details of the quantum chemical computations are described brieff y; then the detailed lines of approach and the treatment of the data for deriving a scheme of contributions (increments) to the conversion energies is proposed. The quantum chemical results are presented and discussed. It is shown that the quantum chemical conversion energies of the imines and pro&mated carbonyl compounds may be built up approximately from phenomelogical contributions associated with characteristic structural fragments. The latter data forms the basis of an analysis of the conversion energies of the geometrical isomers of cytosine and uracif tautomers which will be presented in a subsequent paper. Apparently no quantum chemical data of these model molecules have been reported previously. For the sake of convenience the acyclic imine and 0-protonated compounds treated in ref. 1 are shown in Schemes 3 and 4. COMPUTATfONAL APPROACH AND ADDITIVE MODEL
Quuntum-chemical computations Ab initio self-consistent-field (SCF) cafculations have been carried out in
MimP (Im 5’)
Mim4
Mim3
Mim5 (~1,
stag)
Scheme 1. Model imine derivatives. Miml, propynabimine (propynylidene imine); Mim2, l-pentene-4-yne-3-imine; Mim3, butyne3-imine-aI@-etbynylglyoxal-1-imine); Mim4, l-butynonal diimine (~butyne-1,2~i~ine); Mim5, 1-butyne-3-imine (butynone imine).
XP, ii A H
II H C” 3
C
MpOl
PIP02
Mp04
\
\
MpO3
Mp05
Scheme 2. Model 0-protonated carbonyl compounds. MpOl, propynal (0-protonated); Mp02, 1-pentyne+ene&one; Mp03, butynone; MpO4, butynonal; MpO5, butynone-4-imine.
T.-K. Ha, H.H. GunthurdlJ.
Mol. Struct. (Theo&em)
276 (1992) 187-208
191
'H' ImOl
Im02
Im03
ImN4
/I' / 1 /\ e ImC6
ImC5
ImC7
Scheme 3.
order to determine the equilibrium molecular structures and energies of the relevant model compounds that are imino- and 0-protonated derivatives of propynal, butynone and butynonal. The molecular geometries were optimized with respect to all internal structural parameters (ISPs) by the force method with analytical gradient. The split-valence plus polarization basis sets 6-31G* and 6-31G** [2] were employed throughout. The GAUSSIAN aa [3] program package was used for the ab initio calculations. The optimized geometrical parameters obtained at the HF/6-31G* level agree quite well with those obtained at the HF/6-31G** level of theory,
pool
poo2
poc5 Scheme 4.
poo3
pow
192
T.-K. Ha, H.H. GunthardlJ. Mol. Struct. (Theochem) 276 (1992) 187-208
indicating that inclusion of p-polarization functions on the hydrogen atoms have little influence for the species considered in the present study. In addition, the relative stabilities of the isomers calculated with the two basis sets agree quite well. As a preliminary study a less flexible split-valence basis set (3-21G [4]) was employed for some of the model species and it was found that both the optimized geometrical parameters and the isomerization energies differ quite appreciably from those obtained at the HF/6-31G” or HF/6-31G** levels of theory. In particular, the difference between the energies of the two geometric isomers were much larger with the 3-21G basis set. The results obtained with the 6-31G* or 6-31G** basis set are considered to be more reliable than those obtained with the smaller split-valence basis set. Additivity
model for geometrical
isomer conversion
energies
As was pointed out in the Introduction, the anti-syn electronic conversion energies of both imines and 0-protonated carbonyl compounds depend distinctly on the nature of the fragment C : Z and essentially fall into two categories. This observation suggests that it may be possible to express the conversion energy as the difference of energy terms resulting from the interaction of imino hydrogen atoms (hydroxyl protons) and hydrogen atoms bound to the Cl or C2 atoms; such energy terms may conveniently be denoted by &(HN: l]H * 1) and E,,(HN: l]H * 2). The notation should also indicate the dependence on the fragment C, : Z, e.g. &(HN : l]H * 1112: Z), &,(HN : l]H - 2112: Z). In order to obtain independent estimates for such quantities we used the geometrical isomers of model compounds of the general structure
anti, syn Mim
anti, syn
MimC:Z
(Y = H or CH,; Z = H, H, :CH,, :0 or :NH) and the analogous 0-protonated (isoelectronic) carbonyl compounds. The use of the model compounds, which should provide auxiliary data for the determination of typical contributions to the conversion energies of imine and 0-protonated systems was
T.-K. Ha, H.H. GunthardlJ.
Mol. Struct.
(Theo&em)
276 (1992) 187-208
193
based on the following assumptions: (i) the electronic conversion energy of the process
(2) was identified as the quantity energies of the conversions
E,“,““(HN : 1lH * 1); (ii) analogously,
the
H
(3)
anti
/ i
‘I( ‘\
\
(4)
/
+
x
II ‘II’ ‘a\ ,;\
(5)
were identified as - E,“,““(HN : 1lH * 2112: CH,), - Ela;lx(HN: 1lH * 2112: 0) and - Efy (HN : 1lH * 2 I(2 : NH), respectively; (iii) strictly analogous conventions were applied to the isoelectronic 0-protonated carbonyl compounds. In principle, these conventions introduce a “common” reference configuration for typical energy contributions. Whether the electronic conversion energies of imine and 0-protonated compounds may be rationalized in terms of simple interactions of the form E,, and E,, can only be decided by the success of the approach. In general, the typical contributions (increments) to the electronic conversion energies were determined using the following procedure. (i) The electronic conversion energies of pairs of geometrical isomers of the imine or 0-protonated molecules were considered as basic data for determining the energy increments. (ii) For each geometrical isomer (anti or syn) of a molecule the quantum chemical ground-state total electronic energy was assumed to be built up
of the electronic energy 8mtof a hypothetical ground state, common to both geometrical isomers, but featuring no 1,4, 1,5, etc., type interactions, plus a few such energy contributions:
the latter being characteristic for each geometrical isomer, but common to all members of the imine and/or 0-protonated set, or at least common to each subset characterized by the C2 : Z structural fragment. (iii) The anti 4 syn electronic conversion energy of pairs within the imine and/or 0-protonated set then form condition equations for the determination of the energy contributions:
) SYn
co
(iv) Zeroth-order estimates of El,,, E15, etc., terms were taken from the model compounds. This allows a sufficient number of equations to be obtained for determination of approximate values of the energy contributions either by least-squares or m~irn~-likel~ood techniques, applied to sets or subsets of imine and 0-protonated compounds. In practice, it was required that only a few (l-2) terms of each sort should be introduced, in order to keep the additive model as simple and general as possible. Terms actually used in the present case are listed in Tables 2 and 4, and the equations used for the computation of the terms are given in the section on the analysis of data and discussion. RESULTS
The total energies computed at the HF/6-31G** level of the model imine compounds (see Scheme l), including all the geometrical isomers with respect to the imino group, are listed in Table 1 and the electronic conversion energies thus derived are given in Table 2. The corresponding data for the model 0-protonated carbonyl compounds (see Scheme 2) are given in Tables 3 and 4. Although for the purposes of the present study the optimized internal structural parameters were computed, these data are not reported here. ANALYSIS OF DATA AND DISCUSSION
Electronic energy
of geometrical
The calculated (~F~~3lG*
isomer conversions of model molecules
and ~F~6-3lG**} conversion energies of the
T.-K. Ha, H.H. ~u~t~r~lJ.
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276 fl992) 187-208
195
TABLE 1 The total electronic energies of the geometrical isomers of the model imine compounds Species”
- &$ (a.u.) HF/631G*
Mimls Mimla Mim2s Mim2a Mim3s Mim3a Mim4ss Mim4as Mim4sa Mim4aa Mimfisecl Mim5aecl Mim5sstag MimBastag
HF/6_31G**
169.70253 169.70389 246.58956 246.59277 262.42365 282.42963 26253646 262.58977 262.58437 262.59031 208.74540 208.74305 20374293 20374514
246.60032 246.~3~ 232.43132 282.43722 262.59737 262.60126 262.59539 262.60171 208.75614 20375362 203.75368 206.75593
“See Scheme 1,
TABLE 2 The electronic compounds
energy of conversion
Conversion process”
Mims -+ Mima MimCs -+ MimCa MimOs -3 MimOa MimNss -+ MimNas MimNsa --, MimNaa MimNsa --$MimNss MimNaa --, MimNas Mimsecl -+ Mimaecl Mimsstag -+ Mimastag
of the geometrical
AE%(kcalmol-‘)
Ka,i*b
HF/631G*
HF/631G**
+ -
-
0.85 2.01 3.75 2.08 3.73 1.31 0.34 1.66 1.39
isomers of the imine model
+ -
1.99 3.70 2.13 3.65 1.24 0.28 1.68 1.42
- E;y(HN : 1IH * 1) -~~~(HN:l~H*2~~2:~H~) - E;F(HN : l/H ~2112 : 0) - E,“,“‘(sHN: 1IH ’ 2112:sHN) - Ef?(sHN: 1lH - 2112: aNH) - E;dw(aHN:21H. Z([l:sNH) - E,“w(aHN : 21H * 2111:aNH) - E,“;“(HN : 111:eclCH,) - E,“;“(HN: 111:stagCH,)
“See Scheme 1 for the definition of the geometrical isomers. bThe contribution to the electronic conversion energy AS; of the model conversion process, considered as a first approximation to the corresponding term of the electronic conversion energy of geometrical isomers of the imine compounds.
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Mol. Struct. (T~~~~~
276 (1992) 187-208
TABLE 3 The total electronic energies of the geometrical isomers of the model 0-protonated carbonyl compounds Species” HF/6-31G* MpOs MpOa MpOCs MpOCa MpOsecl MpOaecl MpOsstag MpOastag MpOOs MpOOa MpONss MpONas MpONsa MpONaa
HF/6-31G**
189.84565 189.84705 2~.76257 266.76573 228.96728 228.91013 228.96670 228.90953 302.55242 302.55848 282.72781 282.73096 282.73671 282.74250
228.92151 228.92433 228.92095 228.92372 302.56372 302.~928 282.74283 282.74597 282.75163 282.75707
aSee Scheme 2.
TABLE 4 The electronic energy of conversion of the geometrical isomers of the model 0-protonated carbonyl compounds Conversion process’
MpOs --t MpOa MpOCs --, MpOCa MpOOs --) MpOOa MpONss + MpONas MpONsa + MpONaa MpONsa I+ MpONss MpONaa + MpONas MpOsecl --*MpOaecl MpOsstag --+MpOastag
A&t(kcal mol-‘)
Em,ikbnc
HF/6-31G*
HF/6-31G**
- 0.88 -1.98 - 3.80 - 1.94 - 3.63 + 5.58 + 7.28 - 1.70 - 1.78
_ + f -
3.49 1.97 3.41 5.52 6.97 1.77 1.74
- E,F(pO : l(H * 1) -E:~~O:l~H*Z~~Z:CH~) -E&‘=(pO: l/H * 2112:O) - E,B,“(spO: 1IH - 2112: sHN) - E,“,“(spO : 1IH * 2112: aHN) - E$=(aHN:2lH - 2111:spOlH - 2) - E;*;“(aHN : 21H+2/j1: ap0) - E;F (sp0 : 112: HsCccl) - E;‘,(spO : 112- H&stag)
aSee Scheme 2 for the definition of the geometrical isomers. bNotation for the energy terms identified with A&t of the model conversion process, considered as a first approximation to the corresponding terms of the electronic conversion energy of the geometrical isomers. See text. ‘p denotes a proton.
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(Theochem)
276 (1992) 187-208
197
geometrical isomers of the imines and 0-protonated carbonyl compounds characterized in Schemes 1 and 2 are given in Tables 2 and 4. It can be seen from these data that the two levels of calculation lead to the same conversion energies to within 0.1 kcalmol-l. This difference between the results obtained with the two different levels of calculation is barely relevant to the rationalization of conversion energies in terms of additive contributions, because such models will, in general, achieve only limited accuracy anyway (0.1-0.3 kcal mall’). In the following we use the 6-31G* data to determine the energy contributions to the conversion energies of the geometrical isomers of the model imine and 0-protonated carbonyl compounds. Model imine compounds The energy contribution terms to geometrical isomer conversion energies (Table 2) follow immediately from the assumptions made above according to which the configuration
is postulated to possess a vanishing interaction (Ej$ = 0 for the anti isomer). As a consequence each conversion energy is oppositely equal to exactly one energy contribution term (see Table 2). These terms are denoted by the superscript “aux”. 0-Protonated model compounds The decomposition of the conversion energies of the geometrical isomers of this set of model molecules was done in the same way as for the imine model compounds. Again, the energy of each syn-anti conversion is oppositely equal to one typical energy contribution. Typical terms are shown in Table 4 and such terms are denoted by the superscript “aux”. Additive contribution model for geometrical isomer conversion energies In this section a small set of typical contribution terms is determined, from which the electronic energies of conversion of the geometrical isomers of the acylic imine- and 0-protonated carbonyl compounds treated in ref. 1 can be approximately reconstructed. The contributions were chosen according to the following rules (see above): (i) relevant terms should be perceptible from the structural formula, e.g. 1,4 or 1,5 II-H interactions; (ii) the terms should depend only on either the immediate local structural fragment or, at most, on the next neighbouring region influencing bonding in the local fragment; (iii) the number of relevant contributions for each set
198
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Mol. Struct.
(Theo&em)
276 (1992) 187-208
of molecules should remain small (2-4) and should at least in part be transferable between the different sets; (iv) it should be possible to reconstruct (predict) the conversion energies to within a few tenths of a kilocalorie per mole from the contribution terms. Imines General model. First, a rather general set of equations was formulated by expressing the electronic conversion energies of the imine geometrical isomers additively in terms of contribution terms. The conversion energies were taken from ref. 1 and the contributions were chosen from the structural formula in accordance with eqn. (6) and the rules given above. For the sake of brevity, temporary variable names x,, x2.. . etc., are used in all equations (conversion energies and energy contributions are in kilocalories per mole, and a and s denote the anti and syn isomers, respectively).
aImC
A&, = - &(HN:
sImC
1IH - 1112:CH,)(x,) + E16(HN: 1IH 2112:CH,)(x,) l
x + 0.83
(6)
This condition equation is completed by the zeroth-order estimates for the energy contributions taken from the model compounds (see Table 2): E,,(HN:lIH.lII2:CH,)xE,““=(HN:lIH.l) Z +0.85 EJHN:
1IH - 2112:CH,) x E&“=(HN: l(H
@a) l
2112:CH,)
= 2.01
(gb)
Using the same procedure, the following equations are obtained for the other isomerization processes (see Table 2 and Table 2 of ref. 1).
Abti = + 0.65 x - &(HN
aImed
: 1IH * 1111* eclCH,)(x,)
sImec1
+ &(HN
: 111- eclCH,)(x,)
(10)
T.-K. Ha, H.H. GunthardlJ.
Mol. Struct.
E,,(HN: 1IH * 1111- eclCH,)
(Theo&em)
276 (1992) 187-208
x E,“,““(HN: 1IH - 1) = + 0.85
E,,(HN : 111. eclCH,)
199
(114
x E1B;1X(HN : 111- eclCH,) x + 1.66
Ulb)
\ I,
/e
+
,il
,”
I
I
aImstag
sImstag
A&‘, = + 0.40 : z - E,,(HN : 1IH * 1111* stagCH,)(z,)
+ E,,(HN : 111- stagCH,)(x,)
(12)
E,,(HN : 111- stagCH,) x E,“,““(HN : 1IH * 1) x +0.85
(13a)
E,,(HN : 111- stagCH,) z + 1.39
(13b) /
\ i; ‘I@’ ;I(
+
F;
‘I@/)I(
A&$ = + 0.23 : x - E,,(HN : 111* eclCH,)(x,)
E,,(HN : 111* eclCH,)
x Efr(HN
+ J!&(HN: 1IH - 2112: CH,)(x,)
(14)
: 111. eclCH,)
= 1.66
(15a)
&,(HN : 1IH * 2112: CH,) z E;y(HN : 1IH - 2112: CH,) = 2.01
(15b)
Insertion of the values of the zeroth-order estimates for the contribution terms (Pm values) into the above condition equations shows that the latter are approximately fulfilled. This may be taken as a justification for using the model compounds to evaluate the contribution terms. Equations (9) (15) form a linear system of 12 equations for eight unknowns (Ax = b) the numerical solutions of which are given in Table 5 (8-12 model). It should be noted that A is a sparse matrix. Insertion of the increments into eqns. (9)(15) gives the electronic conversion energies (8t1-8M) to within approximately 0.2 cal mol-l. Special modeb. Inspection of the values given by the general solution shows that the eight contributions X,-X, fulfil within error estimates the
TABLE 6 The energy contributions (in kcal mol-‘) to the imine geometrical isomer conversion energies Contributionn
ModeF Abbrsb
E,,(NH:lIH-1112:CHJ E,,(HN: 1IH .21j2: CH,) E,,(HN : 1IH * l// 1: eclCH,) E,(HN: 111:eclCH,) E,,(HN : IIH - 1 II1. stagCH,) &(HN: 111- stagCH,) E,,(HN : 111* eclCH,) &(HN: 1IH - 2112:CH,)
812d
59”
48f
0.96(11) 1.90(12) OX@) 1.61(5) 0.90(6) 1.34(5) 1.70(5) 1.97(4)
0.99(7)
0.98(6)
1.91(8) 0.99(7) 1.67(?) 0.99(7) 1.38(8) 1.67(7) 1.96(8)
1.90(7) 0.98(6) 1.65(10} 0.98(6) 1.38(10) 1.65(10) 1.90(7)
“See text and Table 2. bShort notation for the contribution terms. ‘Number of unknown terms and equations chosen for the model. dNo conditions between x1 and 3~~.
eq = x, = x,; x4 = x,. fX1= X8= x,; x2 = x,; x1 = x7.
interrelationships: X1x X, w x 5;
x,
=
x7
{model 5-9)
and x,xX,xX,;X~c,xx,;X,~Xx,
(model 4-8)
Least-squares solutions for these two versions are given in Table 5. The following comments seem appropriate: (i) Within the estimated error limits, all three models predict the same values for particular energy contributions; (ii) without a noticeable loss in accuracy, the electronic conversion energies of the imines considered may be expressed by four contributions associated with the nuclear configurations
E,,(HN : l(H - 1) w 0.95(10) E,,(HN: l/H
l
Z//Z: CH,) RS1.90(7)
WW
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(Theochem)
276 (1992) 187-208
201
/
AI,* /
AI/ (b
&(HN
: 111- eclCH,)
x 1.65(10)
(16b)
E,,(HN : 111* stagCH,) z 1.38(10)
From a statistical point of view, the latter two terms should be considered as being different only at a relatively low level of significance. Furthermore, it is obvious that all Eik estimates hold for both the 6-31G* and 6-31G** levels of calculation. Iminoketones If similar reasoning as used for the imine molecules is applied to iminoketones, the following equations and zeroth-order approximations of the contributions to the geometrical isomer conversion energies are obtained (see ref. 1 and Table 2; all energy quantities are in kilocalories per mole). \
N’
N
II
’y
II
+ ’y
aIm0
sIm0
A& = 2.49: z -E,,(HN:llH~1~~2:0)(y,)
+ E1,(HN:11H.2j12:0)(y,)
E,“,““(HN: 1lH * 1) x + 0.85 E;r(HN
: 1lH * 2112: 0) z + 3.75
(17)
A&&= 2.48 : x - E,,(HN * 111* stagCH, 112: 0)( y3) + E,,(HN : l(H . 2112: 0)( y4) E,“,““(HN: 111- stagCH, 112: 0) x + 1.39 E;y(HN : 1lH * 2112: 0) x 3.75
(18)
TABLE 6 The energy contributions (in kcal mol-‘) to the iminoketone geometrical isomer conversion energies Model”
Contribution”
E,(HN:l(H.1112:0) E,,(HN : 1IH * 2112:0) E,,(HN : l/l - stagCH, 112: 0) E&IN : 1IH - 2112: 0) E,,(HN : 1IH - 112: 0) E,,(HN : 112 - stagCH,)
Abbr?
&@
46”
YI yz Y3 Y4 YS Y6
0.99(14) 3.61(14) 1.35(14) 3.79(14) 0.85(17) 4.21(34)
1.02(16) 3.63(14) 1.29(16) 3.66(14) 1.02(16) 4.38(26)
“See text and Table 2. bShort notation for the contribution terms. “Nnmber of unknown terms and equations chosen for the model. dNo conditions between y1 and ys. eY1 = ya; Yz = Y4.
A&,, = 3.36: a - &(HN
: 1IH 1112: 0)( y5) + &(HN l
E,“,“(HN : 1IH - 112: 0) x 0.85
: 112 stagCH,)( ys) l
(19)
Least-squares determination of the energy contribution terms was done in the same way as for imines and leads to the data collected in Table 6, where two models are included. The following comments should be added: (i) both models lead, within error estimates, to equal values of the contribution terms; (ii) within the estimated error limits both models predict the observed conversion energies with equal accuracy; (iii) ab initio electronic energies of the geometrical isomer conversions may be predicted to within 0.1-0.2 kcal mol-l by using four contributions E,,(HN : l(H
l
1) x 1.02(16)
&(HN
: 1IH .2(/Z : 0) ;t 3.68(14)
&(HN
: 111* stagCH, /I2: 0) z 1.29(16)
E16(HN : 112* stagCH, II2 : 0) x 4.38(26) (iv) it is obvious that zeroth-order estimates taken from the model compounds approximate closely the least-squares values of the corresponding energy contributions.
T.-K. Ha, H.H. Gunthard/J.
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203
Diimines The diimines discussed in ref. 1 represent systems where the conversion energy depends on the geometrical isomerism of the neighbouring fragment C2 : Z. Using the electronic conversion energies obtained in ref. 1 and the conventions given in Table 2 of this paper the following condition equations were obtained (all energies are in kilocalories per mole).
ImNaa
A& = + 2.38:
ImNsa ImNas
x - 2E,,(aHN : 1IH 1112: aHN)(z,) + &(sHN l
+ E,,(aHN:2(H-
lIIH*l)l:sHN)(z,) \
N
A& = + 1.08:
: 1IH - 2112: aHN)(z,)
ImNas
(20) N'
ImNss
x - E,,(aHN : 1IH - 112: sHN)(z,) - &,(sHN : 2lH * 11)1: aHN)(z,) + 2E,,(sHN : 1IH - 2112: sHN)(z,)
(21)
In generating definite solutions for the energy contributions in eqns. (20) and (21) there are several choices of additional information. As all of these lead to equivalent solutions within error limits, only one option will be described in detail here. (i) The El4 contribution is assumed to be independent of the nuclear configuration of the second imino group and the value taken from the model compounds is E,“,“(aHN : 1IH * 1) = 0.851.05 kcal mol-‘. (ii) As a zeroth-order approximation for &,(sHN : 1IH * 2112: aHN)(z,) take E,“,““(sHN : 1IH - 212: aHN) x 3.73 kcal mall’ (model compounds MimNsa/aa). (iii) As a zeroth-order approximation to &, (sHN : 1IH - 2 II2 : sHN)(z,) take E,“,““(sHN : 1IH - 2112: sHN) = 2.08 kcal mall’ (model compounds MimNss/as). The corresponding least-squares approximation is given in Table 7, to which the following comments should be added.
204
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TABLE 7 The energy contributions energies
(in kcalmol-‘)
to the diimine geometrical isomer conversion
Contribution”
Abbr?
Model’ %5
E,,(HN: 1IH -1) E,,(sHN: 1IH - 2112:aHN) E,,(sHN: 1IH - 2112:sHN)
21 a, x3
0.8&9.91(33) 3.353.39(33) 2.592.57(31)
“See text and Table 2. bShort notation for the contribution terms ‘Number of unknown contributions and equations chosen for the model.
(i) The diimine geometrical isomer conversion energies may be traced back with acceptable accuracy to three contribution terms. (ii) The 1,4 contribution E14(~1)is essentially the same as that found for imines and iminoketones (0.85-1.05 kcal mol-‘), whilst the 1,5 contributions El5 (z, and z3) depend on the geometrical isomerism of the fragment 2 : HN. If the latter has an anti nuclear configuration, the El6 term is nearly the same as that for fragment 2 : 0 (iminoketones); if it has a syn nuclear configuration it is only slightly higher than that found for fragment 2 : CH, (imines). Obviously the diimines may be taken as a paradigm for the dependence of type El5 (repulsive) contributions on the geometrical isomerism of the fragment 2 : Z. Summary of the additive contribution terms to the geometrical isomer conversion energies Inspection of the data collected in Tables 5-7 suggests the following statements. (i) In general, the isomer conversion energies of the model compounds (Schemes 1 and 2) studied seem to provide reliable zeroth-order approximations to typical 1,4 and 1,5 H-H contribution terms in the set of imines, iminoketones and diimines studied in ref. 1. (ii) Some of the contributions are essentially equal for the three classes of compounds; this can be seen from Table 8 where species are grouped together according to the value of a specific contribution term. (iii) Table 8 shows that the conversion energies of the complete set of geometrical isomers may approximately be expressed by, at most, three contributions selected from a set of 4-6 terms according to simple rules; the terms are easily perceptible from the schematic structural formula of the two isomers.
T.-K. Ha, H.H. Gu~thard/~.
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276 (1992) 187-208
205
TABLE 8 Summary of the typical contributions to the electronic conversion energies of imine geometrical isomers Contribution
1,4 H-H interactions (E,,)
Value (kcal mol-*)
Typical nuclear configuration H \
1.0(15)
j
Classes of compounds CH, eclipsed or staggered, HC:CH,, HC:CO, HC : NH anti or syn
H/ k
1,5 II-II interactions (E,J
1.99(12)
1.65(11)
1.38(10) 1.29(7)
1,6 II-II interactions (E&
3.7(2)
ImO
3.8(3)
ImN
2.5(3)
ImN
4.4(2)
IlllO
206
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276 (1932) 187-238
O-protonated carbonyl compounds An evaluation of the contributions to the electronic conversion energies of 0-protonated carbonyl compounds can be made along similar lines as for the imine species. The basis of the approach comprises the geometrical isomer conversion energies of the model compounds listed in Scheme 2 (Table 4) and the conversion energies reported in ref. 1 (Table 3). Leastsquares treatment of the data yields the energy contributions presented in Table 9, which should be complemented by the following statements. (i) Both of the 1,4 HXI contributions Z&(spO: 11H * 1) and El4 (&IN : 1IH - 1) are assumed to be independent of the substituent at C2. To a first approximation these data (+ 0.88 and O.&S1.05 kcal mol-‘) were taken over from the model compounds or from the imine compounds. (ii) All the 1,5 II-H contributions were assumed to depend on the structural element C2: Z; for Z = HN, moreover, they were assumed to depend on the geometrical isomerism of this fragment. (iii) The values of the energy contributions (increments) listed in Table 9 may be derived for either a subset or the full set of 0-protonated carbonyl compounds treated in ref. 1; within error estimates the resulting values were found to be equal. (iv) In close analogy with the imines, the conversion energies taken from the model compounds are reasonably accurate zeroth-order approximations of the energy contributions to the conversion energies of the * 1 r_ ___-..- _PLl_- A --^L_--L--l i-__?:__ geometrical isomers 01 me v-procomibeu sytmea. The comments made in the preceding section also apply to the results obtained for the 0-protonated compounds. Comparison of imine and 0-protonated carbonyl compounds Comparison of the data in Tables 8 and 9 reveals that the isoelectronic imine and 0-protonated carbonyl compounds studied in ref. 1 behave quite similarly, not only with respect to their geometrical isomer conversion energies, but also in terms of their 1,4 and 1,5 H-H repulsive contributions. For both sets of compounds contributions of analogous type and number with fairly similar magnitudes apply. Conversion energies may be reconstructed for the two sets to within 0.2-0.3 kcalmoll’. For speculative predictions, higher unce~ainties might be expected. For such applications the number of different contributions might be reduced considerably at the expense of accuracy. As suggested by Tables 8 and 9, taking error estimates into account, one might occasionally work with just one value for El4 contributions and two or three values for E,, interactions, depending on the fragment C2 : Z.
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Mol. Struct.
(Theo&em)
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207
TABLE 9 Summary of the typical contributions to the electronic conversion energies of the geometrical isomers of 0-protonated carbonyl compounds Contribution
Value (kcal mol-‘)
Typical nuclear configuration
Classes of compounds (R)
1.1(2)
CH, eclipsed or staggered, HC : CH,, HC : CO, HC : NH anti or syn
E,, (sHN : 1IH - 1)
l.cuq15)
CH, eclipsed or staggered, HC : CH,, HC : CO, HC : NH anti or syn
1,5 I-&H interactions (EIs)
1.71(25)
Acetaldehyde
1.37(25)
POC
3.7(2)
PO0
3.4(2)
PON
1,4 l+H interactions (I&) (sp0 : 1IH - 1)
1.9(3)
1,6 KH interaction (E,,)
4.5(l)
PO0
CONCLUSION
It has been shown that the energies of conversion of the geometrical isomers of simple acyclic imines and 0-protonated carbonyl compounds may be built up additively from (repulsive) 1,4 and 1,5 HN interaction contributions of approximately 0.2-0.3 kcal malll. The 1,4 contributions are essentially independent of the neighbouring structural fragments, whilst the 1,5 interactions depend in a characteristic way on these. All the contributions show close agreement between the imine and protonated species. Furthermore, only a few contributions are required to predict the electronic conversion energies of the geometrical isomers of species related to the acyclic imines and protonated carbonyl compounds, for which the present repulsive contributions were derived. In a forthcoming paper we will show that these contributions may be used to rationalize the electronic conversion energies of the geometrical isomers of a considerable number of tautomers of cytosine and uracil, provided one further characteristic type of interaction is introduced. ACKNOWLEDGEMENTS
The authors thank the ETH Zurich a~inistration for their generous provision of computer time and other resources. We also thank Pars K. Gunthard for typing the manuscript. REFERENCES 1 T.-K. Ha and H.H. Gunthard, J. Mol. Struct. (Theochem), 259 (1992) 229. 2 P.C. Harriharan and J.A. Pople, Theor. Chim. Acta, 28 (1973) 213. 3 M.J. Frisch, M. Head-Gordon, H.B. Schlegel, K. Raghavachari, J.S. Binkley, C. Gonzalez, D.J. Defrees, D.J. Fox, R.A. Whiteside, R. Seeger, C.F. Melius, J. Baker, R.L. Martin, R.L. Kahn, J.J.P. Stewart, E.M. Fluder, S. Topios and J.A. Pople, GAUSSIAN 88,Gaussian Inc., Pittsburgh, PA, 1988. 4 J.S. Binkley, J.A. Pople and W.J. Hehre, J. Am. Chem. Sot., 102 (1939) 93.
187
Ab initio stability study of the geometric isomerism of acyclic imines and 0-protonated carbonyl compounds. Part II. Model compounds for additive schemes of anti-syn conversion energies: imino- and 0-protonated derivatives of propynal, butynone and butynonal T.-K. Ha and H.H. Gunthard Physical
Chemistry Laboratory,
ETH Zentrum,
CH-8092 Zurich (Switzerland)
(Received 28 January 1992)
Abstract The problem of decomposing the conversion energies of the geometrical isomers of acyclic isoelectronic imines and 0-protonated carbonyl compounds into intuitive contributions associated with the repulsive intramolecular interactions of imino hydrogen atoms (hydroxyl hydrogen atoms) with hydrogen atoms bound to neighbouring carbon atoms is considered. The investigation was based on quantum chemical computations at the HartreeFock level with the 6-31G* and 6-31G** basis sets for 14 acyclic imines, 14 0-protonated carbonyl species, 10 model imines and 10 model 0-protonated systems. Definitions of specific (1,4 and 1,5) hydrogen contributions (E,, and E,,) and rules for decomposing the conversion energies into additive contributions are proposed. Application of the procedure to the geometrical isomers of model compounds (imines HCC*CH:NH, HCC.C(:NH).CH:CH,, HC!C.C(:NH)CHO, HC:C*C(:NH)CH:NH, HC:C.C(:NH)CH,, and 0-protonated species HCiC*CH:Op, HCiC.C(:Op)CH:CH,, HCC.C(:Op)CH, HCIC.C(:Op)CH:O and HCC.C(:Op)CH:NH) (p denotes a proton) gives zeroth-order estimates of particular contributions. These estimates were used to determine a set of specific contributions, which in turn permit one to reconstruct the conversion energies of the geometrical isomers of acyclic isoelectronic imines and 0-protonated carbonyl compounds by using a simple additive scheme. The conversion energies were reproduced to within 0.2-0.3 kcal mall’. The contribution terms are expected to be fairly generally applicable.
INTRODUCTION
In a recent paper a quantum chemical investigation (Hartree-Fock
(HF)
6-31G* or second-order Moller-Plesset (MP2) 6-31G**//6-31G** level) of the Correspondence to: H.H. Gunthard, Physical Chemistry Laboratory, ETH Zentrum, CH8992 Zurich, Switzerland.
0166-1280/92/$05.00 0 1992 Elsevier Science Publishers
B.V. All rights reserved.
188
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Mol. Struct. (Theo&em)
276 (1992) 187-208
correlation between the geometrical isomerism of simple acyclic isoelectronic imines and 0-protonated carbonyl compounds of the structural types (X, Y = H or CH,; Z = CH,, 0 or NH; p denotes a proton)
hP,
lH/
iCl
ri Cl
X
Y /\ / X
NY
/ \
c2
c2
(1)
II 2
II z
0-protonated types p0 anti ClC2 p0 syn ClC2
Imine types HN anti ClC2 HN syn ClC2
and the total electronic energy and internal structural parameters (bond length and bond angles) has been reported [l]. Of the results obtained in that study, the following should be briefly ment’ ,M_e;r;)m~e a-nzb;;; isomers with Z = :CH, or of the type HN=C\ < 0.5 kcalmolll than HN syn isomers; (ii) HN anti ClC2 isomers with Z = :0 or :NH are more stable by > 2 kcal mall’; (iii) conversion from anti to syn isomers implies a narrowing of L NC,X( L OC,X) and a widening of L NC, C, ( L OC, C,) by 2 5’; (iv) L HNC,, L pOC, and L XC, C, are nearly independent of the geometrical isomerism of the imino (0-protonated carbonyl) group; (v) anti-syn conversion causes the d(l3-N) (d(p0)) bond length to increase slightly (2mA); d(Cl-C2) increases by 4-5 mA and d(X(C,)-C,) decreases by approximately 4mA (X = H or CH,). Furthermore, the data obtained on these imines and 0-protonated carbonyl compounds suggest that the anti-syn conversion energies, e.g. of the process H \
/” iiy
X/ anti
y
ii
+ X’
y 71’
vn
are composed of additive contributions of the type El4(H . . . X> or El5{H . . . Y}, i.e. of 1,4 or 1,5 l3-H interactions of Urey-Bradley type. However, from the data derived in that study it was not possible to arrive at approximate numerical values for such contributions. The derivation of energy increments in order to estimate conversion energies seems to be of some general interest. A typical case of interest is the relatively large set of geometrical isomers of the various tautomers of the nucleic acid bases, where experimental determination of the equilibria of all tautomeric forms including
the geometrical isomerism of hydroxyl and imino groups might be difficult. Although quantum chemical calculation of the relative stabilities of such a set of isomers is complicated by the intricacies of basis-set dependence, it might, on grounds of experience, be expected that the basis-set dependence of the conversion energies of geometrical isomers will remain tolerable, provided these are computed at a sufficiently high level. Analogously, the changes in the internal structural parameters associated with geometrical isomer conversion have been found to depend only slightly on the basis sets 3-21G to 63IG** (see ref. 1). In this paper we first present quantum chemical optimized energy and optimized structural data of a set of model compounds. The calculations were done using HF/6-31G” and HF/6-31G** basis sets, The model compounds (essentially derivatives of propynoic acid HC : C * COOH) 0
were chosen such that the conversion energies of the geometrical isomers would serve as reference and additional energy data for determining a system of additive contributions to the electronic conversion energies of the imines and 0-protonated carbonyl compounds studied in ref. 1. Schemes 1 and 2 show the schematic formulae of the molecules chosen. The details of the quantum chemical computations are described brieff y; then the detailed lines of approach and the treatment of the data for deriving a scheme of contributions (increments) to the conversion energies is proposed. The quantum chemical results are presented and discussed. It is shown that the quantum chemical conversion energies of the imines and pro&mated carbonyl compounds may be built up approximately from phenomelogical contributions associated with characteristic structural fragments. The latter data forms the basis of an analysis of the conversion energies of the geometrical isomers of cytosine and uracif tautomers which will be presented in a subsequent paper. Apparently no quantum chemical data of these model molecules have been reported previously. For the sake of convenience the acyclic imine and 0-protonated compounds treated in ref. 1 are shown in Schemes 3 and 4. COMPUTATfONAL APPROACH AND ADDITIVE MODEL
Quuntum-chemical computations Ab initio self-consistent-field (SCF) cafculations have been carried out in
MimP (Im 5’)
Mim4
Mim3
Mim5 (~1,
stag)
Scheme 1. Model imine derivatives. Miml, propynabimine (propynylidene imine); Mim2, l-pentene-4-yne-3-imine; Mim3, butyne3-imine-aI@-etbynylglyoxal-1-imine); Mim4, l-butynonal diimine (~butyne-1,2~i~ine); Mim5, 1-butyne-3-imine (butynone imine).
XP, ii A H
II H C” 3
C
MpOl
PIP02
Mp04
\
\
MpO3
Mp05
Scheme 2. Model 0-protonated carbonyl compounds. MpOl, propynal (0-protonated); Mp02, 1-pentyne+ene&one; Mp03, butynone; MpO4, butynonal; MpO5, butynone-4-imine.
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276 (1992) 187-208
191
'H' ImOl
Im02
Im03
ImN4
/I' / 1 /\ e ImC6
ImC5
ImC7
Scheme 3.
order to determine the equilibrium molecular structures and energies of the relevant model compounds that are imino- and 0-protonated derivatives of propynal, butynone and butynonal. The molecular geometries were optimized with respect to all internal structural parameters (ISPs) by the force method with analytical gradient. The split-valence plus polarization basis sets 6-31G* and 6-31G** [2] were employed throughout. The GAUSSIAN aa [3] program package was used for the ab initio calculations. The optimized geometrical parameters obtained at the HF/6-31G* level agree quite well with those obtained at the HF/6-31G** level of theory,
pool
poo2
poc5 Scheme 4.
poo3
pow
192
T.-K. Ha, H.H. GunthardlJ. Mol. Struct. (Theochem) 276 (1992) 187-208
indicating that inclusion of p-polarization functions on the hydrogen atoms have little influence for the species considered in the present study. In addition, the relative stabilities of the isomers calculated with the two basis sets agree quite well. As a preliminary study a less flexible split-valence basis set (3-21G [4]) was employed for some of the model species and it was found that both the optimized geometrical parameters and the isomerization energies differ quite appreciably from those obtained at the HF/6-31G” or HF/6-31G** levels of theory. In particular, the difference between the energies of the two geometric isomers were much larger with the 3-21G basis set. The results obtained with the 6-31G* or 6-31G** basis set are considered to be more reliable than those obtained with the smaller split-valence basis set. Additivity
model for geometrical
isomer conversion
energies
As was pointed out in the Introduction, the anti-syn electronic conversion energies of both imines and 0-protonated carbonyl compounds depend distinctly on the nature of the fragment C : Z and essentially fall into two categories. This observation suggests that it may be possible to express the conversion energy as the difference of energy terms resulting from the interaction of imino hydrogen atoms (hydroxyl protons) and hydrogen atoms bound to the Cl or C2 atoms; such energy terms may conveniently be denoted by &(HN: l]H * 1) and E,,(HN: l]H * 2). The notation should also indicate the dependence on the fragment C, : Z, e.g. &(HN : l]H * 1112: Z), &,(HN : l]H - 2112: Z). In order to obtain independent estimates for such quantities we used the geometrical isomers of model compounds of the general structure
anti, syn Mim
anti, syn
MimC:Z
(Y = H or CH,; Z = H, H, :CH,, :0 or :NH) and the analogous 0-protonated (isoelectronic) carbonyl compounds. The use of the model compounds, which should provide auxiliary data for the determination of typical contributions to the conversion energies of imine and 0-protonated systems was
T.-K. Ha, H.H. GunthardlJ.
Mol. Struct.
(Theo&em)
276 (1992) 187-208
193
based on the following assumptions: (i) the electronic conversion energy of the process
(2) was identified as the quantity energies of the conversions
E,“,““(HN : 1lH * 1); (ii) analogously,
the
H
(3)
anti
/ i
‘I( ‘\
\
(4)
/
+
x
II ‘II’ ‘a\ ,;\
(5)
were identified as - E,“,““(HN : 1lH * 2112: CH,), - Ela;lx(HN: 1lH * 2112: 0) and - Efy (HN : 1lH * 2 I(2 : NH), respectively; (iii) strictly analogous conventions were applied to the isoelectronic 0-protonated carbonyl compounds. In principle, these conventions introduce a “common” reference configuration for typical energy contributions. Whether the electronic conversion energies of imine and 0-protonated compounds may be rationalized in terms of simple interactions of the form E,, and E,, can only be decided by the success of the approach. In general, the typical contributions (increments) to the electronic conversion energies were determined using the following procedure. (i) The electronic conversion energies of pairs of geometrical isomers of the imine or 0-protonated molecules were considered as basic data for determining the energy increments. (ii) For each geometrical isomer (anti or syn) of a molecule the quantum chemical ground-state total electronic energy was assumed to be built up
of the electronic energy 8mtof a hypothetical ground state, common to both geometrical isomers, but featuring no 1,4, 1,5, etc., type interactions, plus a few such energy contributions:
the latter being characteristic for each geometrical isomer, but common to all members of the imine and/or 0-protonated set, or at least common to each subset characterized by the C2 : Z structural fragment. (iii) The anti 4 syn electronic conversion energy of pairs within the imine and/or 0-protonated set then form condition equations for the determination of the energy contributions:
) SYn
co
(iv) Zeroth-order estimates of El,,, E15, etc., terms were taken from the model compounds. This allows a sufficient number of equations to be obtained for determination of approximate values of the energy contributions either by least-squares or m~irn~-likel~ood techniques, applied to sets or subsets of imine and 0-protonated compounds. In practice, it was required that only a few (l-2) terms of each sort should be introduced, in order to keep the additive model as simple and general as possible. Terms actually used in the present case are listed in Tables 2 and 4, and the equations used for the computation of the terms are given in the section on the analysis of data and discussion. RESULTS
The total energies computed at the HF/6-31G** level of the model imine compounds (see Scheme l), including all the geometrical isomers with respect to the imino group, are listed in Table 1 and the electronic conversion energies thus derived are given in Table 2. The corresponding data for the model 0-protonated carbonyl compounds (see Scheme 2) are given in Tables 3 and 4. Although for the purposes of the present study the optimized internal structural parameters were computed, these data are not reported here. ANALYSIS OF DATA AND DISCUSSION
Electronic energy
of geometrical
The calculated (~F~~3lG*
isomer conversions of model molecules
and ~F~6-3lG**} conversion energies of the
T.-K. Ha, H.H. ~u~t~r~lJ.
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276 fl992) 187-208
195
TABLE 1 The total electronic energies of the geometrical isomers of the model imine compounds Species”
- &$ (a.u.) HF/631G*
Mimls Mimla Mim2s Mim2a Mim3s Mim3a Mim4ss Mim4as Mim4sa Mim4aa Mimfisecl Mim5aecl Mim5sstag MimBastag
HF/6_31G**
169.70253 169.70389 246.58956 246.59277 262.42365 282.42963 26253646 262.58977 262.58437 262.59031 208.74540 208.74305 20374293 20374514
246.60032 246.~3~ 232.43132 282.43722 262.59737 262.60126 262.59539 262.60171 208.75614 20375362 203.75368 206.75593
“See Scheme 1,
TABLE 2 The electronic compounds
energy of conversion
Conversion process”
Mims -+ Mima MimCs -+ MimCa MimOs -3 MimOa MimNss -+ MimNas MimNsa --, MimNaa MimNsa --$MimNss MimNaa --, MimNas Mimsecl -+ Mimaecl Mimsstag -+ Mimastag
of the geometrical
AE%(kcalmol-‘)
Ka,i*b
HF/631G*
HF/631G**
+ -
-
0.85 2.01 3.75 2.08 3.73 1.31 0.34 1.66 1.39
isomers of the imine model
+ -
1.99 3.70 2.13 3.65 1.24 0.28 1.68 1.42
- E;y(HN : 1IH * 1) -~~~(HN:l~H*2~~2:~H~) - E;F(HN : l/H ~2112 : 0) - E,“,“‘(sHN: 1IH ’ 2112:sHN) - Ef?(sHN: 1lH - 2112: aNH) - E;dw(aHN:21H. Z([l:sNH) - E,“w(aHN : 21H * 2111:aNH) - E,“;“(HN : 111:eclCH,) - E,“;“(HN: 111:stagCH,)
“See Scheme 1 for the definition of the geometrical isomers. bThe contribution to the electronic conversion energy AS; of the model conversion process, considered as a first approximation to the corresponding term of the electronic conversion energy of geometrical isomers of the imine compounds.
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TABLE 3 The total electronic energies of the geometrical isomers of the model 0-protonated carbonyl compounds Species” HF/6-31G* MpOs MpOa MpOCs MpOCa MpOsecl MpOaecl MpOsstag MpOastag MpOOs MpOOa MpONss MpONas MpONsa MpONaa
HF/6-31G**
189.84565 189.84705 2~.76257 266.76573 228.96728 228.91013 228.96670 228.90953 302.55242 302.55848 282.72781 282.73096 282.73671 282.74250
228.92151 228.92433 228.92095 228.92372 302.56372 302.~928 282.74283 282.74597 282.75163 282.75707
aSee Scheme 2.
TABLE 4 The electronic energy of conversion of the geometrical isomers of the model 0-protonated carbonyl compounds Conversion process’
MpOs --t MpOa MpOCs --, MpOCa MpOOs --) MpOOa MpONss + MpONas MpONsa + MpONaa MpONsa I+ MpONss MpONaa + MpONas MpOsecl --*MpOaecl MpOsstag --+MpOastag
A&t(kcal mol-‘)
Em,ikbnc
HF/6-31G*
HF/6-31G**
- 0.88 -1.98 - 3.80 - 1.94 - 3.63 + 5.58 + 7.28 - 1.70 - 1.78
_ + f -
3.49 1.97 3.41 5.52 6.97 1.77 1.74
- E,F(pO : l(H * 1) -E:~~O:l~H*Z~~Z:CH~) -E&‘=(pO: l/H * 2112:O) - E,B,“(spO: 1IH - 2112: sHN) - E,“,“(spO : 1IH * 2112: aHN) - E$=(aHN:2lH - 2111:spOlH - 2) - E;*;“(aHN : 21H+2/j1: ap0) - E;F (sp0 : 112: HsCccl) - E;‘,(spO : 112- H&stag)
aSee Scheme 2 for the definition of the geometrical isomers. bNotation for the energy terms identified with A&t of the model conversion process, considered as a first approximation to the corresponding terms of the electronic conversion energy of the geometrical isomers. See text. ‘p denotes a proton.
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197
geometrical isomers of the imines and 0-protonated carbonyl compounds characterized in Schemes 1 and 2 are given in Tables 2 and 4. It can be seen from these data that the two levels of calculation lead to the same conversion energies to within 0.1 kcalmol-l. This difference between the results obtained with the two different levels of calculation is barely relevant to the rationalization of conversion energies in terms of additive contributions, because such models will, in general, achieve only limited accuracy anyway (0.1-0.3 kcal mall’). In the following we use the 6-31G* data to determine the energy contributions to the conversion energies of the geometrical isomers of the model imine and 0-protonated carbonyl compounds. Model imine compounds The energy contribution terms to geometrical isomer conversion energies (Table 2) follow immediately from the assumptions made above according to which the configuration
is postulated to possess a vanishing interaction (Ej$ = 0 for the anti isomer). As a consequence each conversion energy is oppositely equal to exactly one energy contribution term (see Table 2). These terms are denoted by the superscript “aux”. 0-Protonated model compounds The decomposition of the conversion energies of the geometrical isomers of this set of model molecules was done in the same way as for the imine model compounds. Again, the energy of each syn-anti conversion is oppositely equal to one typical energy contribution. Typical terms are shown in Table 4 and such terms are denoted by the superscript “aux”. Additive contribution model for geometrical isomer conversion energies In this section a small set of typical contribution terms is determined, from which the electronic energies of conversion of the geometrical isomers of the acylic imine- and 0-protonated carbonyl compounds treated in ref. 1 can be approximately reconstructed. The contributions were chosen according to the following rules (see above): (i) relevant terms should be perceptible from the structural formula, e.g. 1,4 or 1,5 II-H interactions; (ii) the terms should depend only on either the immediate local structural fragment or, at most, on the next neighbouring region influencing bonding in the local fragment; (iii) the number of relevant contributions for each set
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of molecules should remain small (2-4) and should at least in part be transferable between the different sets; (iv) it should be possible to reconstruct (predict) the conversion energies to within a few tenths of a kilocalorie per mole from the contribution terms. Imines General model. First, a rather general set of equations was formulated by expressing the electronic conversion energies of the imine geometrical isomers additively in terms of contribution terms. The conversion energies were taken from ref. 1 and the contributions were chosen from the structural formula in accordance with eqn. (6) and the rules given above. For the sake of brevity, temporary variable names x,, x2.. . etc., are used in all equations (conversion energies and energy contributions are in kilocalories per mole, and a and s denote the anti and syn isomers, respectively).
aImC
A&, = - &(HN:
sImC
1IH - 1112:CH,)(x,) + E16(HN: 1IH 2112:CH,)(x,) l
x + 0.83
(6)
This condition equation is completed by the zeroth-order estimates for the energy contributions taken from the model compounds (see Table 2): E,,(HN:lIH.lII2:CH,)xE,““=(HN:lIH.l) Z +0.85 EJHN:
1IH - 2112:CH,) x E&“=(HN: l(H
@a) l
2112:CH,)
= 2.01
(gb)
Using the same procedure, the following equations are obtained for the other isomerization processes (see Table 2 and Table 2 of ref. 1).
Abti = + 0.65 x - &(HN
aImed
: 1IH * 1111* eclCH,)(x,)
sImec1
+ &(HN
: 111- eclCH,)(x,)
(10)
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Mol. Struct.
E,,(HN: 1IH * 1111- eclCH,)
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x E,“,““(HN: 1IH - 1) = + 0.85
E,,(HN : 111. eclCH,)
199
(114
x E1B;1X(HN : 111- eclCH,) x + 1.66
Ulb)
\ I,
/e
+
,il
,”
I
I
aImstag
sImstag
A&‘, = + 0.40 : z - E,,(HN : 1IH * 1111* stagCH,)(z,)
+ E,,(HN : 111- stagCH,)(x,)
(12)
E,,(HN : 111- stagCH,) x E,“,““(HN : 1IH * 1) x +0.85
(13a)
E,,(HN : 111- stagCH,) z + 1.39
(13b) /
\ i; ‘I@’ ;I(
+
F;
‘I@/)I(
A&$ = + 0.23 : x - E,,(HN : 111* eclCH,)(x,)
E,,(HN : 111* eclCH,)
x Efr(HN
+ J!&(HN: 1IH - 2112: CH,)(x,)
(14)
: 111. eclCH,)
= 1.66
(15a)
&,(HN : 1IH * 2112: CH,) z E;y(HN : 1IH - 2112: CH,) = 2.01
(15b)
Insertion of the values of the zeroth-order estimates for the contribution terms (Pm values) into the above condition equations shows that the latter are approximately fulfilled. This may be taken as a justification for using the model compounds to evaluate the contribution terms. Equations (9) (15) form a linear system of 12 equations for eight unknowns (Ax = b) the numerical solutions of which are given in Table 5 (8-12 model). It should be noted that A is a sparse matrix. Insertion of the increments into eqns. (9)(15) gives the electronic conversion energies (8t1-8M) to within approximately 0.2 cal mol-l. Special modeb. Inspection of the values given by the general solution shows that the eight contributions X,-X, fulfil within error estimates the
TABLE 6 The energy contributions (in kcal mol-‘) to the imine geometrical isomer conversion energies Contributionn
ModeF Abbrsb
E,,(NH:lIH-1112:CHJ E,,(HN: 1IH .21j2: CH,) E,,(HN : 1IH * l// 1: eclCH,) E,(HN: 111:eclCH,) E,,(HN : IIH - 1 II1. stagCH,) &(HN: 111- stagCH,) E,,(HN : 111* eclCH,) &(HN: 1IH - 2112:CH,)
812d
59”
48f
0.96(11) 1.90(12) OX@) 1.61(5) 0.90(6) 1.34(5) 1.70(5) 1.97(4)
0.99(7)
0.98(6)
1.91(8) 0.99(7) 1.67(?) 0.99(7) 1.38(8) 1.67(7) 1.96(8)
1.90(7) 0.98(6) 1.65(10} 0.98(6) 1.38(10) 1.65(10) 1.90(7)
“See text and Table 2. bShort notation for the contribution terms. ‘Number of unknown terms and equations chosen for the model. dNo conditions between x1 and 3~~.
eq = x, = x,; x4 = x,. fX1= X8= x,; x2 = x,; x1 = x7.
interrelationships: X1x X, w x 5;
x,
=
x7
{model 5-9)
and x,xX,xX,;X~c,xx,;X,~Xx,
(model 4-8)
Least-squares solutions for these two versions are given in Table 5. The following comments seem appropriate: (i) Within the estimated error limits, all three models predict the same values for particular energy contributions; (ii) without a noticeable loss in accuracy, the electronic conversion energies of the imines considered may be expressed by four contributions associated with the nuclear configurations
E,,(HN : l(H - 1) w 0.95(10) E,,(HN: l/H
l
Z//Z: CH,) RS1.90(7)
WW
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276 (1992) 187-208
201
/
AI,* /
AI/ (b
&(HN
: 111- eclCH,)
x 1.65(10)
(16b)
E,,(HN : 111* stagCH,) z 1.38(10)
From a statistical point of view, the latter two terms should be considered as being different only at a relatively low level of significance. Furthermore, it is obvious that all Eik estimates hold for both the 6-31G* and 6-31G** levels of calculation. Iminoketones If similar reasoning as used for the imine molecules is applied to iminoketones, the following equations and zeroth-order approximations of the contributions to the geometrical isomer conversion energies are obtained (see ref. 1 and Table 2; all energy quantities are in kilocalories per mole). \
N’
N
II
’y
II
+ ’y
aIm0
sIm0
A& = 2.49: z -E,,(HN:llH~1~~2:0)(y,)
+ E1,(HN:11H.2j12:0)(y,)
E,“,““(HN: 1lH * 1) x + 0.85 E;r(HN
: 1lH * 2112: 0) z + 3.75
(17)
A&&= 2.48 : x - E,,(HN * 111* stagCH, 112: 0)( y3) + E,,(HN : l(H . 2112: 0)( y4) E,“,““(HN: 111- stagCH, 112: 0) x + 1.39 E;y(HN : 1lH * 2112: 0) x 3.75
(18)
TABLE 6 The energy contributions (in kcal mol-‘) to the iminoketone geometrical isomer conversion energies Model”
Contribution”
E,(HN:l(H.1112:0) E,,(HN : 1IH * 2112:0) E,,(HN : l/l - stagCH, 112: 0) E&IN : 1IH - 2112: 0) E,,(HN : 1IH - 112: 0) E,,(HN : 112 - stagCH,)
Abbr?
&@
46”
YI yz Y3 Y4 YS Y6
0.99(14) 3.61(14) 1.35(14) 3.79(14) 0.85(17) 4.21(34)
1.02(16) 3.63(14) 1.29(16) 3.66(14) 1.02(16) 4.38(26)
“See text and Table 2. bShort notation for the contribution terms. “Nnmber of unknown terms and equations chosen for the model. dNo conditions between y1 and ys. eY1 = ya; Yz = Y4.
A&,, = 3.36: a - &(HN
: 1IH 1112: 0)( y5) + &(HN l
E,“,“(HN : 1IH - 112: 0) x 0.85
: 112 stagCH,)( ys) l
(19)
Least-squares determination of the energy contribution terms was done in the same way as for imines and leads to the data collected in Table 6, where two models are included. The following comments should be added: (i) both models lead, within error estimates, to equal values of the contribution terms; (ii) within the estimated error limits both models predict the observed conversion energies with equal accuracy; (iii) ab initio electronic energies of the geometrical isomer conversions may be predicted to within 0.1-0.2 kcal mol-l by using four contributions E,,(HN : l(H
l
1) x 1.02(16)
&(HN
: 1IH .2(/Z : 0) ;t 3.68(14)
&(HN
: 111* stagCH, /I2: 0) z 1.29(16)
E16(HN : 112* stagCH, II2 : 0) x 4.38(26) (iv) it is obvious that zeroth-order estimates taken from the model compounds approximate closely the least-squares values of the corresponding energy contributions.
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276 (1992) 187-208
203
Diimines The diimines discussed in ref. 1 represent systems where the conversion energy depends on the geometrical isomerism of the neighbouring fragment C2 : Z. Using the electronic conversion energies obtained in ref. 1 and the conventions given in Table 2 of this paper the following condition equations were obtained (all energies are in kilocalories per mole).
ImNaa
A& = + 2.38:
ImNsa ImNas
x - 2E,,(aHN : 1IH 1112: aHN)(z,) + &(sHN l
+ E,,(aHN:2(H-
lIIH*l)l:sHN)(z,) \
N
A& = + 1.08:
: 1IH - 2112: aHN)(z,)
ImNas
(20) N'
ImNss
x - E,,(aHN : 1IH - 112: sHN)(z,) - &,(sHN : 2lH * 11)1: aHN)(z,) + 2E,,(sHN : 1IH - 2112: sHN)(z,)
(21)
In generating definite solutions for the energy contributions in eqns. (20) and (21) there are several choices of additional information. As all of these lead to equivalent solutions within error limits, only one option will be described in detail here. (i) The El4 contribution is assumed to be independent of the nuclear configuration of the second imino group and the value taken from the model compounds is E,“,“(aHN : 1IH * 1) = 0.851.05 kcal mol-‘. (ii) As a zeroth-order approximation for &,(sHN : 1IH * 2112: aHN)(z,) take E,“,““(sHN : 1IH - 212: aHN) x 3.73 kcal mall’ (model compounds MimNsa/aa). (iii) As a zeroth-order approximation to &, (sHN : 1IH - 2 II2 : sHN)(z,) take E,“,““(sHN : 1IH - 2112: sHN) = 2.08 kcal mall’ (model compounds MimNss/as). The corresponding least-squares approximation is given in Table 7, to which the following comments should be added.
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276 (1992) 187-208
TABLE 7 The energy contributions energies
(in kcalmol-‘)
to the diimine geometrical isomer conversion
Contribution”
Abbr?
Model’ %5
E,,(HN: 1IH -1) E,,(sHN: 1IH - 2112:aHN) E,,(sHN: 1IH - 2112:sHN)
21 a, x3
0.8&9.91(33) 3.353.39(33) 2.592.57(31)
“See text and Table 2. bShort notation for the contribution terms ‘Number of unknown contributions and equations chosen for the model.
(i) The diimine geometrical isomer conversion energies may be traced back with acceptable accuracy to three contribution terms. (ii) The 1,4 contribution E14(~1)is essentially the same as that found for imines and iminoketones (0.85-1.05 kcal mol-‘), whilst the 1,5 contributions El5 (z, and z3) depend on the geometrical isomerism of the fragment 2 : HN. If the latter has an anti nuclear configuration, the El6 term is nearly the same as that for fragment 2 : 0 (iminoketones); if it has a syn nuclear configuration it is only slightly higher than that found for fragment 2 : CH, (imines). Obviously the diimines may be taken as a paradigm for the dependence of type El5 (repulsive) contributions on the geometrical isomerism of the fragment 2 : Z. Summary of the additive contribution terms to the geometrical isomer conversion energies Inspection of the data collected in Tables 5-7 suggests the following statements. (i) In general, the isomer conversion energies of the model compounds (Schemes 1 and 2) studied seem to provide reliable zeroth-order approximations to typical 1,4 and 1,5 H-H contribution terms in the set of imines, iminoketones and diimines studied in ref. 1. (ii) Some of the contributions are essentially equal for the three classes of compounds; this can be seen from Table 8 where species are grouped together according to the value of a specific contribution term. (iii) Table 8 shows that the conversion energies of the complete set of geometrical isomers may approximately be expressed by, at most, three contributions selected from a set of 4-6 terms according to simple rules; the terms are easily perceptible from the schematic structural formula of the two isomers.
T.-K. Ha, H.H. Gu~thard/~.
Mol. Street. ~~~~rn~
276 (1992) 187-208
205
TABLE 8 Summary of the typical contributions to the electronic conversion energies of imine geometrical isomers Contribution
1,4 H-H interactions (E,,)
Value (kcal mol-*)
Typical nuclear configuration H \
1.0(15)
j
Classes of compounds CH, eclipsed or staggered, HC:CH,, HC:CO, HC : NH anti or syn
H/ k
1,5 II-II interactions (E,J
1.99(12)
1.65(11)
1.38(10) 1.29(7)
1,6 II-II interactions (E&
3.7(2)
ImO
3.8(3)
ImN
2.5(3)
ImN
4.4(2)
IlllO
206
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MOE.Struct. ~T~~~~)
276 (1932) 187-238
O-protonated carbonyl compounds An evaluation of the contributions to the electronic conversion energies of 0-protonated carbonyl compounds can be made along similar lines as for the imine species. The basis of the approach comprises the geometrical isomer conversion energies of the model compounds listed in Scheme 2 (Table 4) and the conversion energies reported in ref. 1 (Table 3). Leastsquares treatment of the data yields the energy contributions presented in Table 9, which should be complemented by the following statements. (i) Both of the 1,4 HXI contributions Z&(spO: 11H * 1) and El4 (&IN : 1IH - 1) are assumed to be independent of the substituent at C2. To a first approximation these data (+ 0.88 and O.&S1.05 kcal mol-‘) were taken over from the model compounds or from the imine compounds. (ii) All the 1,5 II-H contributions were assumed to depend on the structural element C2: Z; for Z = HN, moreover, they were assumed to depend on the geometrical isomerism of this fragment. (iii) The values of the energy contributions (increments) listed in Table 9 may be derived for either a subset or the full set of 0-protonated carbonyl compounds treated in ref. 1; within error estimates the resulting values were found to be equal. (iv) In close analogy with the imines, the conversion energies taken from the model compounds are reasonably accurate zeroth-order approximations of the energy contributions to the conversion energies of the * 1 r_ ___-..- _PLl_- A --^L_--L--l i-__?:__ geometrical isomers 01 me v-procomibeu sytmea. The comments made in the preceding section also apply to the results obtained for the 0-protonated compounds. Comparison of imine and 0-protonated carbonyl compounds Comparison of the data in Tables 8 and 9 reveals that the isoelectronic imine and 0-protonated carbonyl compounds studied in ref. 1 behave quite similarly, not only with respect to their geometrical isomer conversion energies, but also in terms of their 1,4 and 1,5 H-H repulsive contributions. For both sets of compounds contributions of analogous type and number with fairly similar magnitudes apply. Conversion energies may be reconstructed for the two sets to within 0.2-0.3 kcalmoll’. For speculative predictions, higher unce~ainties might be expected. For such applications the number of different contributions might be reduced considerably at the expense of accuracy. As suggested by Tables 8 and 9, taking error estimates into account, one might occasionally work with just one value for El4 contributions and two or three values for E,, interactions, depending on the fragment C2 : Z.
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(Theo&em)
276 (1992) 187-208
207
TABLE 9 Summary of the typical contributions to the electronic conversion energies of the geometrical isomers of 0-protonated carbonyl compounds Contribution
Value (kcal mol-‘)
Typical nuclear configuration
Classes of compounds (R)
1.1(2)
CH, eclipsed or staggered, HC : CH,, HC : CO, HC : NH anti or syn
E,, (sHN : 1IH - 1)
l.cuq15)
CH, eclipsed or staggered, HC : CH,, HC : CO, HC : NH anti or syn
1,5 I-&H interactions (EIs)
1.71(25)
Acetaldehyde
1.37(25)
POC
3.7(2)
PO0
3.4(2)
PON
1,4 l+H interactions (I&) (sp0 : 1IH - 1)
1.9(3)
1,6 KH interaction (E,,)
4.5(l)
PO0
CONCLUSION
It has been shown that the energies of conversion of the geometrical isomers of simple acyclic imines and 0-protonated carbonyl compounds may be built up additively from (repulsive) 1,4 and 1,5 HN interaction contributions of approximately 0.2-0.3 kcal malll. The 1,4 contributions are essentially independent of the neighbouring structural fragments, whilst the 1,5 interactions depend in a characteristic way on these. All the contributions show close agreement between the imine and protonated species. Furthermore, only a few contributions are required to predict the electronic conversion energies of the geometrical isomers of species related to the acyclic imines and protonated carbonyl compounds, for which the present repulsive contributions were derived. In a forthcoming paper we will show that these contributions may be used to rationalize the electronic conversion energies of the geometrical isomers of a considerable number of tautomers of cytosine and uracil, provided one further characteristic type of interaction is introduced. ACKNOWLEDGEMENTS
The authors thank the ETH Zurich a~inistration for their generous provision of computer time and other resources. We also thank Pars K. Gunthard for typing the manuscript. REFERENCES 1 T.-K. Ha and H.H. Gunthard, J. Mol. Struct. (Theochem), 259 (1992) 229. 2 P.C. Harriharan and J.A. Pople, Theor. Chim. Acta, 28 (1973) 213. 3 M.J. Frisch, M. Head-Gordon, H.B. Schlegel, K. Raghavachari, J.S. Binkley, C. Gonzalez, D.J. Defrees, D.J. Fox, R.A. Whiteside, R. Seeger, C.F. Melius, J. Baker, R.L. Martin, R.L. Kahn, J.J.P. Stewart, E.M. Fluder, S. Topios and J.A. Pople, GAUSSIAN 88,Gaussian Inc., Pittsburgh, PA, 1988. 4 J.S. Binkley, J.A. Pople and W.J. Hehre, J. Am. Chem. Sot., 102 (1939) 93.