The influence of the second methyl group position on the chemical shifts values of all protons in dimethylalkane molecules in the 1 H NMR spectra

The protons chemical shifts values in the PMR spectra of dimethylalkanes of general formula N,N-n (when n is the letter designation of linear alkane, and N, N are the carbon atom numbers which are attached to the methyl groups in the alkyl chain of n) have analyzed. It is calculated and discussed the individual (N,N-n-i), the arithmetic means (N,N-n-i) “standard” differential parameters (the difference between absorption of studied proton in N,N-n and its absorption in the n) and the "integral spectral changes” Σ N,N-n-i that occur in process n → N,N-n). Also it is calculated and discussed the individual (N,N-n’-i) and the arithmetic means (N,N-n’-i) additional differential parameters (the difference between absorption of studied proton in N,N-n and its absorption in the correspondent monomethylalkane Nn) of dimethylalkanes N,N-n.


Introduction 1.General comments
In a previous report [1], we describe the results of the study of chemical shift values of all protons in the monomethylalkanes molecules.The next step is planned to study the effect of the introduction of a second methyl group in the alkyl chain of the monomethylalkanes on NMR spectral parameters of resulted dimethylalkanes molecules.It was shown for all the studied types of monomethylalkanes that the introduction of a methyl group at different positions of the alkyl chain leads to approximately the same result: significantly changed only proton chemical shifts of the so-called "tetracarbonic fragment" [-С n-1 Н n- 1 2 -С n Н n (С n' Н n' 3 )-С n+1 Н n+1 2 -].There are two such "tetracarbon fragments" in dimethylalkanes molecules.It is interesting to examine the change in the PMR spectra as the result of the interaction between these fragments when they change their relative position in the molecule.

Objects of research
Generally designated each molecule of dimethylalkane ««N 1 ,N 2 -n» consists of two parts: the first two numeric of the N 1 and N 2 (N 2 ≥ N 1 ) separated by commas indicates the position of two methyl groups in the alkyl chain (i.e., specified family of dimethylalkanes).Then, with a hyphen small letter indicate the name of the alkane.Numbering started with the shortest chain of methane ("a"), although among considered dimethylalkanes there are no derivative of methane "a" and ethane «b».The symbol "c" denotes propane, «d»-butane, «e»-pentane, «f»-hexane, «g» -heptane and «h»-octane.The different isomers of dimethylalkanes are formed depending on the occurrence place of both methyl groups in the chain («N 1 » and «N using instruments with different frequency: low-frequency (90 MHz) and high-frequency (300 or 400 MHz)."Low-frequency" parameter was used only in the absence of "high-frequency" value.The authors of data represented in [2] give their own attribution of spectra signals to the absorption of definite types of hydrogen atom nuclei.The authors of data represented in [3] (which are usually given up to 0.01 ppm) do not give their own attribution of spectra signals; therefore we do this by ourselves.
All signals of each of the 1 H NMR spectra of every of dimethylalkane N 1 ,N 2 -n are arranged in a fairly narrow (1 ppm) range values δ Н : from 0.70 ppm to 1.70 ppm The most easily interpreted are triplet signals of methyl end groups, the signals middle methyl groups (doublets) and the singlet signals of six protons in gem-dimethyl groups (or of nine protons in the compounds 2,2-n).The assignment of the multiplet signals of methylene and methine protons is often difficult, because usually in the range of magnitudes 1.0 ÷ 1.4 ppm these signals overlap, especially at long chain methylalkanes. 1 * The "literary" values of aliphatic protons absorption of dimethylalkanes of 2,N 2 -n, 3,N 2 -n and 4,N 2n families, denoted above as "δ Н,N1,N2-n і ", are shown in tables 1-4 situated at the beginning of some sections.These values are called by us the basic spectral parameters (shortly, BSP) of protons absorption.If the BSP value (δ Н,N1,N2-n і ) is used in both sources [2 and 3] , both figures given in the table.Also, in some tables re-are shown BSP values for previously cited data of the compounds with reverse numbered carbon chain.Such "reversibly numbered" compounds indicated in Tables by an asterisk (see below).
Every cell of the every Table has two values of BSP given as a fraction: numerator (without parentheses) is a value, taken from [3], and denominator (with parentheses) is the same parameter but taken from [2].When the source [2] instead of discrete values of the "i-type" protons signals give a numeric range, in the Table is a dash "(-)" and the footnote number, which identifies the boundaries of the interval.The same symbol "(-)" (without the footnote) we use in numerator where it is difficult to us to assign discrete value to proton absorption in data represented in [3] for substance N 1 ,N 2 -n.In some cases (for example, in Table 1), along with authors [2] assignment of spectra signal shown in [2] we present our own assignment of these signals.In this case, a separate line (under a line that describes the author's [2] assignment) of the corresponding numerals from our assignment are given in square brackets in bold.
The calculated values of differential spectral parameters (shortly «DSP»), referred to as Δδ Н,N1,N2-n i , along with the BSP values used for the convenience in discussing of the results.About DSP in detail we will say below.DSP values are always given with the "+" or "-" sign, they should be expressed in billionths parts (shortly, mlrd.), calculated from the equation: 1 ppm = 1000 mlrd.When calculating the values of DSP all BSP values of compounds 2,N-n -4,N-n, taken from [2 and 3], are rounded to the nearest number divisible by 0.005 ppm.We estimate the inaccuracy of measurements as ± 0.02 ppm (20 mlrd., see below).

Discussion of results
As mentioned above, the chemical shift of the studied proton (i.e., its BSP) in the common designation system referred to as "δ Н,N1,N2-n i " with using an superscript and subscript symbols.For convenience to simplify the designation due to the failure of an superscript and subscript symbols, in this report we introduce a new system of designation for each parameter δ Н,N1,N2-n i .In each case the new introduced designation is duplicated the old one (i.e., with using of common superscript and subscript symbols such as "δ Н,N1,N2-n i ").The BSP values ("δ Н,N1,N2-n i ") in the text and Tables 1 -4 are marked with italic black bold font as "N 1 ,N 2 -n-B-i".The symbol "B" indicates that this parameter is basic (BSP), and it introduced in order to distinguish the basic parameter from similar abbreviations for the differential spectral parameters (DSP).In the above example of the 2,5-dimethyloktane 2,5-h the symbol «2,5-h-В-5'» (δ Н,2,5-h 5' ) denotes the magnitude of the chemical shift of the methyl protons H-5' of "far end" methyl group -С 5' Н 5' 3 .For all or most of the compounds of each the families dimethylalkanes N 1 ,N 2 -n we calculated the arithmetic mean value [1] of the discussed parameter referred to as the underlined 1 * In some cases, we could not reliably attribute some signals in spectra available of [3] to absorption of the specific methylene (or methine) protons.Therefore, the basis of our research is the signal assignment in the spectra given in [2] and performed by the authors [2].The correctness of the findings made by us in this study largely depends on the correctness of these assignments.Validation of our own attribution of spectra signals represented in [3] we see in the consistency of the data given in .
The difference between the chemical shift of the every i-th proton in discussed dimethylalkane N 1 ,N 2 -n and the same i-th type of protons in the "standard compound", which we denote as (etal), we designate as the differential spectral parameter «Δδ Н,N1,N2-n i » (abbreviated DSP).Depending on tasks it may be selected the different reference compounds.The DSP parameters of all of the discussed dimethylalkanes N 1 ,N 2 -n are calculated for each of the i-type proton as follows: Δδ Н,N1,N2-n і = δ Н,N1,N2-n іδ Н,etal i , and in our proposed system of notation as : It is known that in every linear alkanes are present only two types of "one-carbonic fragment».There are the "end methyl group" and "mid methylene group".For protons of these groups previously [1], we determine the average values of BSP.There are (rounded to the nearest number divisible by 0.005 ppm), respectively, 0.880 ppm and 1.270 ppm.Therefore, as "standard compound" for comparison of the reference parameter BSP of "triprotonic" signal of each of the methyl groups in the investigated dimethylalkanes N 1 ,N 2 -n we shall use the "standard reference parameter" -an averaged BSP value of "end methyl groups" protons in the long-chain linear alkane (designated as «δ Н end.»).We denote this parameter as etal-СН 3 = 0.880 ppm.For comparison of methylene and methine protons we use as a "standard reference parameter" (by analogy with the methyl groups) an average BSP value of "mid methylene groups" protons in long-chain linear alkanes «δ Н mid.».We denote it as etal-СН 2 = 1.270ppm.These type of DSP values we named as 'standard' and denote a shorter red bold italic symbol: (DSP In addition to "standard" DSP sometimes be used other "additional" type of DSP, with blue color and with a stroke, that is, DSP' = N 1 ,N 2 -n'-i.As the "etalon" compound to calculate this type of DSP we usually use the "family" of corresponding monomethyl alkanes.As the value of "etalon parameter" is usually taken is the arithmetic mean of BSP, which in [1] is designated as N-B-i.Hence: DSP' = N 1

,N 2 -n-B-i -N-n-B-i.
The measurement error of BSP values is adopted by us equal to 20mlrd.So the BSP values of methyl groups fall into the "strip " values equal to etal-СН 3 = 0.880 ppm ± 0.020 ppm (i.e., in the range from 0.860 ppm to 0.900 ppm) and values of methylene groups BSP fall into the "strip" values etal-СН 2 = 1.270 ppm ± 0.020 ppm (i.e., in the range from 1.250 ppm to 1.290 ppm) should be considered as "insufficiently valid" 2* .Hence the differential parameters of DSP and DSP', which are in absolute value less than or equal to 20 mlrd., either not at all be discussed, or in the discussion will be considered as" insufficiently valid".
NMR 1 H spectra of 2,N-dimethylalkanes which contain the most "remote" second methyl group (at N 2 = 6), were considered first.Then, gradually , "bringing closer" a second methyl group to first one we reach to the "vic-location" in the 2,3-dimethylalkanes 2,3-n and finally to the "gem-location" in the 2,2dimethylalkanes 2,2-n.In both this families of 2,N-dimethylalkanes is expected no significantly impact the second methyl group on the values of BSP studied fragments.
Table 1 The base spectral parameters(BSP) values, i.e. δ Н,2,6-n i chemical shifts of i-type protons of 2,6dimethylalkanes 2,6-n of the general formula Number of compound formula The (BSP) values («δ Н,2,6-n i ») in ppm of specified number of "i-type" protons denoted in brackets.In parenthesis below is shown the signal multiplicity.
Continuation of Table 1 Num -ber of compound Formula The (BSP) values («δ Н,2,6-n i ») in ppm of specified number of "i-type" protons denoted in brackets.In parenthesis below is shown the signal multiplicity.Let us comment the values of some BSP and the calculated values of DSP and DSP'.The values of six methyl protons (three H-1 and three H-2') in mono-2-methylalkanes 2n and 2,6-dimethylalkanes 2,6-n are approximately the same and equal to 0.870 ppm.Hence the value of «standard» DSP is also approximately the same and so the values of "additional » DSP' are practically zero.The BSP parameters of methine proton H-2 doublet signal (BSP ≈ 1.520 ppm) in 2,6-dimethylalkanes 2,6-n also are virtually unchanged compared to similar signals in mono-2-methylalkanes 2n.Namely, the introduction of additional methyl group to the C-6 atom, as expected, almost no effect on the BSP values of molecule fragment comprising atoms C-1 -C-2 (i.e., six methyl H-1 and H-2' protons and a methine proton H-2), since the second methyl group (N 2 = 6) is too far from the considered protons to have a marked effect on their BSP values.
For asymmetrical 2,5-dimethylheptane 2,5-g there are all only 4 digits in We consider these values as "estimated" ones for the spectral parameters of 2,5-g-B-i.Therefore, when discussing the results will use them gently, mainly to confirm some dependencies which are detected for the symmetrical 2,5-dimethylhexane 2,5-f parameters.
The BSP values of multiplet methine proton signal H-2 in both 2,5-dimethylalkanes 2,5-n spectra, shown in [2], are different.The figure of 2,5-f-B-2 = 2,5-f-B-5 = 1.48 ppm of symmetrical 2.5dimethylhexane 2,5-f seems to be more correct.The figure of 2,5-g-B-2 = 2,5-g-B-5 = 1.39 ppm of 2.5dimethylheptane 2,5-g [2] (remember, it is one of only four for figures in the whole spectrum!)seems less plausible.The reason is that, since it is the same as for H-2 and H-5, which seems doubtful in the light of the findings for monomethylalkanes [1].It can be assumed that this figure is an average value between the BSP values of low-field multiplet signals of the proton H-2(e.g., 2,5-g-B-2 ≈ 1.50 ppm) and more highfield value [e.g., 2,5-g-B-5 ≈ 1.30 ppm] of proton H-5 signal.The latter figure corresponds to approximately BSP values of methine protons H-3 in the 3-monomethylalkanes 3n [1], which are the objects for comparison with BSP values doublet signal of the proton H-5 in 2.5-dimethylheptane 2,5-g.
Although, in fact, the estimative nature of the BSP values of methylene groups С 3 Н 3 2 protons in both 2,5-dimethylalkanes 2,5-f and 2,5-g (and methylene groups С 4 Н 4 2 protons in symmetrical 2.5dimethylhexane 2,5-f) we can do the cautious conclusion.It seems likely that the introduction of additional methyl group to the C-5 atom in the 2-methylalkanes 2n only slightly changes (or does not change at all) the value of these protons BSP.That is, both of interest 2 -](where n = 2 and 5) substantially do not affect each other.
In the spectra of 2,4-dimethylalkanes 2,4-n of the general formula: 3 both "tetracarbonic fragment" we are interested in superimposed on one another, so far as they have a common methylene group -С 3 Н 3 2 -.Therefore, for the family of 2,4-dimethylalkanes 2,4-n we can expected the mutual influence of two closely spaced methyl groups (at C-2 and C-4) on the BSP values of studied in this section molecule fragment C-1 -C-6, especially on the protons H-3.

Formula
The BSP values («δ Н,2,4-n i ») in ppm of specified number of "i-type" protons denoted in brackets.In parenthesis below is shown the signal multiplicity.

Formula
The (BSP) values («δ Н,2,2-n i ») in ppm of specified number of "i-type" protons denoted in brackets.In parenthesis below is shown the signal multiplicity.The spectral data of following 2,2-dimethylalkanes 2,2-n: 2,2-d, 2,2-h and possibly, 2,2-f we submitted as the most reliable.In the spectrum of 2,2-dimethylpentane 2,2-e, given in [2], the methylene protons H-3 and H-4 BSP values are equal to each other (2,2-e-B-3 = 2,2-e-B-4 = 1.18 ppm), which is in doubt.Our interpretation of the compounds 2,2-e and 2,2-f spectra, described in [3], is not reliably grounded, so in Table 4 either is an interval (as for 2,2-f),or a particularly questionable figures, accompanied by three question marks (as for 2,2-e) The spectrum of 2,2-dimethylpropane 2,2-c is obtained in carbon tetrachloride [2] and is given merely as illustrative material, and therefore it will not be discussed.Due to the lack of carbon chain length beginning from C-4 (single atom C-4) in unsymmetrical 2,2-dimethylbutane 2,2-d, the compound 2,2-d (as well as 2,2-c), we believe as the branched alkanes and not as linear ones and therefore we believe the protons BSP value in them are not typical for a family of 2,2-dimethylalkanes 2,2-n.
Let us consider the spectra of "atypical" shortchain 2,2-dimethylbutane 2,2-d, then the spectra of the "typical", midchain 2,2-dimethylpentane 2,2-e and then the spectra of two "truly longchain" 2,2dimethylalkanes 2,2-f and 2,2-h.Below we show that the last three spectrum are useful to viewed together, and it is for them to calculate the arithmetic mean parameters.
The NMR 1 H spectra of 3,N-dimethylalkanes which are available to us and contain the most "remote" second methyl group (at N 2 = 7), were considered first.Then, as in the case 2,N-dimethylalkanes 2,N-n, gradually, "bringing closer" a second methyl group to first one we reach to the "vic-location" in the 3,4-dimethylalkanes 3,4-n and finally to the "gem-location" in the 3,3-dimethylalkanes 3,3-n.

2. 1. The family of 3,7-dimethylalkanes 3,7-n.
The only representative of a 3,7-dimethylalkanes 3,7-n, NMR spectra of which is given in the sources we use [2,3], is the above-considered 2,6-dimethyloctane 2,6-h, indicated by reverse numbering as "3,7dimethyloctane 3,7-h».In the reverse numbering of the carbon atoms of the alkyl chain of 2,6-h the methyl group at C-2 (in direct numbering), becomes the methyl group at C-7 (in reverse numbering), and the methyl group at C-6 (in direct numbering), becomes the methyl group at C-3 (in reverse numbering).
Given this, we can conclude that the introduction of second methyl groups instead of hydrogen atoms at carbon C-7along with the existing methyl groups at carbon C-3 (to form the 3,7-dimethylalkanes 3,7-n by reverse numbering) as expected, almost no effect on the absorption of the fragment C-1 -C-4 (by reverse numbering) protons.
For the symmetrical 3,5-dimethylheptane 3,5-g PMR spectrum the authors [2] led an unique attribution the proton signals.They identified two stereoisomers in spectrum and attribute every signal to each of these isomers protons.For the spectrum of 3,5-dimethyloctane 3,5-h authors [2] referring of signals are not informative, so this spectrum will not be commented on.The second isomer of symmetrical 3,5-dimethylheptane 3,5-g2.The values of base 3,5-g2-B-i and the "standard" differential 3,5-g2-I parameters of second isomer of the symmetrical 3,5-dimethylheptane

3 Н 3 2 and С 4 Н 4 2
but both of these parameters fall into the "strip of insufficiently validity values" (i.e., in the range from 1.25 ppm up to 1.29 ppm).Therefore it is possible to formulate the following cautious conclusion.Simultaneous introduction of two methyl groups instead of two hydrogen atoms at carbonC-2 of ethyl moiety converts the C-1 -C-2 dicarbonic fragment into substituted tert-butyl group.The BSP values of methylene groups С dimethylbutane 2,2-d the BSP value (2,2-d-B-3 = 1.220 ppm, 2,2-d-3 = -50mlrd.) is reliably established, this parameter is not regarded as informative, since because too short carbon chain molecule protons H-3 exposed so called "end effects influence".