From Roush et al. (2007) Figure 7 Average of Long k values Frequency Imaginary (cm-1) Index 4.000000000000000e+3 1.803700000000000e-3 3.996000000000000e+3 1.831400000000000e-3 3.992000000000000e+3 1.859800000000000e-3 3.988000000000000e+3 1.888800000000000e-3 3.984000000000000e+3 1.918700000000000e-3 3.980000000000000e+3 1.949200000000000e-3 3.976000000000000e+3 1.980600000000000e-3 3.972000000000000e+3 2.012700000000000e-3 3.968000000000000e+3 2.045700000000000e-3 3.964000000000000e+3 2.079500000000000e-3 3.960000000000000e+3 2.114300000000000e-3 3.956000000000000e+3 2.150000000000000e-3 3.952000000000000e+3 2.186500000000000e-3 3.948000000000000e+3 2.224200000000000e-3 3.944000000000000e+3 2.262800000000000e-3 3.940000000000000e+3 2.302500000000000e-3 3.936000000000000e+3 2.343400000000000e-3 3.932000000000000e+3 2.385400000000000e-3 3.928000000000000e+3 2.428500000000000e-3 3.924000000000000e+3 2.473000000000000e-3 3.920000000000000e+3 2.518700000000000e-3 3.916000000000000e+3 2.565800000000000e-3 3.912000000000000e+3 2.614200000000000e-3 3.908000000000000e+3 2.664200000000000e-3 3.904000000000000e+3 2.715600000000000e-3 3.900000000000000e+3 2.768700000000000e-3 3.896000000000000e+3 2.823400000000000e-3 3.892000000000000e+3 2.879800000000000e-3 3.888000000000000e+3 2.938000000000000e-3 3.884000000000000e+3 2.998100000000000e-3 3.880000000000000e+3 3.060100000000000e-3 3.876000000000000e+3 3.124200000000000e-3 3.872000000000000e+3 3.190400000000000e-3 3.868000000000000e+3 3.258900000000000e-3 3.864000000000000e+3 3.329700000000000e-3 3.860000000000000e+3 3.402900000000000e-3 3.856000000000000e+3 3.478800000000000e-3 3.852000000000000e+3 3.557300100000000e-3 3.848000000000000e+3 3.638600000000000e-3 3.844000000000000e+3 3.722900000000000e-3 3.840000000000000e+3 3.810300000000000e-3 3.836000000000000e+3 3.901000000000000e-3 3.832000000000000e+3 3.995100000000000e-3 3.828000000000000e+3 4.092900000000000e-3 3.824000000000000e+3 4.194400000000000e-3 3.820000000000000e+3 4.300000000000000e-3 3.816000000000000e+3 4.409800000000000e-3 3.812000000000000e+3 4.524100000000000e-3 3.808000000000000e+3 4.643100000000000e-3 3.804000000000000e+3 4.779800000000000e-3 3.800000000000000e+3 4.907000000000000e-3 3.796000000000000e+3 5.035100000000000e-3 3.792000000000000e+3 5.164000000000000e-3 3.788000000000000e+3 5.327200000000000e-3 3.784000000000000e+3 5.458000000000000e-3 3.780000000000000e+3 5.623200000000000e-3 3.776000000000000e+3 5.789300000000000e-3 3.772000000000000e+3 5.989900000000000e-3 3.768000000000000e+3 6.158300000000000e-3 3.764000000000000e+3 6.361100000000000e-3 3.760000000000000e+3 6.565200000000000e-3 3.756000000000000e+3 6.770700000000000e-3 3.752000000000000e+3 7.010700000000000e-3 3.748000000000000e+3 7.252200000000000e-3 3.744000000000000e+3 7.495200000000000e-3 3.740000000000000e+3 7.739700000000000e-3 3.736000000000000e+3 8.019200000000000e-3 3.732000000000000e+3 8.333700000000000e-3 3.728000000000000e+3 8.650000000000000e-3 3.724000000000000e+3 8.968200000000002e-3 3.720000000000000e+3 9.321800000000000e-3 3.716000000000000e+3 9.710699999999998e-3 3.712000000000000e+3 1.010000000000000e-2 3.708000000000000e+3 1.050000000000000e-2 3.704000000000000e+3 1.100000000000000e-2 3.700000000000000e+3 1.150000000000000e-2 3.696000000000000e+3 1.200000000000000e-2 3.692000000000000e+3 1.250000000000000e-2 3.688000000000000e+3 1.310000000000000e-2 3.684000000000000e+3 1.380000000000000e-2 3.680000000000000e+3 1.450000000000000e-2 3.676000000000000e+3 1.520000000000000e-2 3.672000000000000e+3 1.600000000000000e-2 3.668000000000000e+3 1.690000100000000e-2 3.664000000000000e+3 1.790000000000000e-2 3.660000000000000e+3 1.900000000000000e-2 3.656000000000000e+3 2.010000000000000e-2 3.652000000000000e+3 2.140000000000000e-2 3.648000000000000e+3 2.280000000000000e-2 3.644000000000000e+3 2.430000000000000e-2 3.640000000000000e+3 2.600000000000000e-2 3.636000000000000e+3 2.790000000000000e-2 3.632000000000000e+3 3.000000000000000e-2 3.628000000000000e+3 3.240000000000000e-2 3.624000000000000e+3 3.510000000000000e-2 3.620000000000000e+3 3.810000000000000e-2 3.616000000000000e+3 4.160000000000000e-2 3.612000000000000e+3 4.550000000000000e-2 3.608000000000000e+3 5.010000000000000e-2 3.604000000000000e+3 5.530000000000000e-2 3.600000000000000e+3 6.140000000000000e-2 3.596000000000000e+3 6.860000099999999e-2 3.592000000000000e+3 7.690000000000000e-2 3.588000000000000e+3 8.670000000000000e-2 3.584000000000000e+3 9.830000000000000e-2 3.580000000000000e+3 1.118000000000000e-1 3.576000000000000e+3 1.276000000000000e-1 3.572000000000000e+3 1.457000000000000e-1 3.568000000000000e+3 1.662000000000000e-1 3.564000000000000e+3 1.887000000000000e-1 3.560000000000000e+3 2.126000000000000e-1 3.556000000000000e+3 2.370000000000000e-1 3.552000000000000e+3 2.605000000000000e-1 3.548000000000000e+3 2.816000000000000e-1 3.544000000000000e+3 2.982000000000000e-1 3.540000000000000e+3 3.083000000000000e-1 3.536000000000000e+3 3.102000000000000e-1 3.532000000000000e+3 3.028000000000000e-1 3.528000000000000e+3 2.869000000000000e-1 3.524000000000000e+3 2.647000000000000e-1 3.520000000000000e+3 2.392000000000000e-1 3.516000000000000e+3 2.133000000000000e-1 3.512000000000000e+3 1.891000000000000e-1 3.508000000000000e+3 1.677000000000000e-1 3.504000000000000e+3 1.494000000000000e-1 3.500000000000000e+3 1.343000000000000e-1 3.496000000000000e+3 1.221000000000000e-1 3.492000000000000e+3 1.124000000000000e-1 3.488000000000000e+3 1.049000000000000e-1 3.484000000000000e+3 9.940000000000000e-2 3.480000000000000e+3 9.570000000000000e-2 3.476000000000000e+3 9.360000000000000e-2 3.472000000000000e+3 9.310000000000000e-2 3.468000000000000e+3 9.410000000000000e-2 3.464000000000000e+3 9.660000000000000e-2 3.460000000000000e+3 1.009000000000000e-1 3.456000000000000e+3 1.069000000000000e-1 3.452000000000000e+3 1.149000000000000e-1 3.448000000000000e+3 1.250000000000000e-1 3.444000000000000e+3 1.374000000000000e-1 3.440000000000000e+3 1.522000000000000e-1 3.436000000000000e+3 1.691000000000000e-1 3.432000000000000e+3 1.878000000000000e-1 3.428000000000000e+3 2.073000000000000e-1 3.424000000000000e+3 2.264000000000000e-1 3.420000000000000e+3 2.436000000000000e-1 3.416000000000000e+3 2.568000000000000e-1 3.412000000000000e+3 2.642000000000000e-1 3.408000000000000e+3 2.643000000000000e-1 3.404000000000000e+3 2.564000000000000e-1 3.400000000000000e+3 2.414000000000000e-1 3.396000000000000e+3 2.212000000000000e-1 3.392000000000000e+3 1.985000000000000e-1 3.388000000000000e+3 1.755000100000000e-1 3.384000000000000e+3 1.538000000000000e-1 3.380000000000000e+3 1.343000000000000e-1 3.376000000000000e+3 1.173000000000000e-1 3.372000000000000e+3 1.028000000000000e-1 3.368000000000000e+3 9.040000000000000e-2 3.364000000000000e+3 7.990000000000000e-2 3.360000000000000e+3 7.090000000000001e-2 3.356000000000000e+3 6.340000000000000e-2 3.352000000000000e+3 5.690000000000000e-2 3.348000000000000e+3 5.130000000000000e-2 3.344000000000000e+3 4.660000000000000e-2 3.340000000000000e+3 4.240000000000000e-2 3.336000000000000e+3 3.880000000000000e-2 3.332000000000000e+3 3.560000000000000e-2 3.328000000000000e+3 3.280000000000000e-2 3.324000000000000e+3 3.040000000000000e-2 3.320000000000000e+3 2.820000000000000e-2 3.316000000000000e+3 2.620000000000000e-2 3.312000000000000e+3 2.450000000000000e-2 3.308000000000000e+3 2.290000000000000e-2 3.304000000000000e+3 2.150000000000000e-2 3.300000000000000e+3 2.020000000000000e-2 3.296000000000000e+3 1.900000000000000e-2 3.292000000000000e+3 1.790000000000000e-2 3.288000000000000e+3 1.700000000000000e-2 3.284000000000000e+3 1.610000000000000e-2 3.280000000000000e+3 1.520000000000000e-2 3.276000000000000e+3 1.450000000000000e-2 3.272000000000000e+3 1.380000000000000e-2 3.268000000000000e+3 1.310000000000000e-2 3.264000000000000e+3 1.250000000000000e-2 3.260000000000000e+3 1.200000000000000e-2 3.256000000000000e+3 1.150000000000000e-2 3.252000000000000e+3 1.100000000000000e-2 3.248000000000000e+3 1.050000000000000e-2 3.244000000000000e+3 1.010000000000000e-2 3.240000000000000e+3 9.708800000000000e-3 3.236000000000000e+3 9.341500000000002e-3 3.232000000000000e+3 8.976700000000000e-3 3.228000000000000e+3 8.647800000000000e-3 3.224000000000000e+3 8.354600000000000e-3 3.220000000000000e+3 8.063600000000000e-3 3.216000000000000e+3 7.774800000000000e-3 3.212000000000000e+3 7.521400000000000e-3 3.208000000000000e+3 7.269900000000000e-3 3.204000000000000e+3 7.053600000000000e-3 3.200000000000000e+3 6.805800000000000e-3 3.196000000000000e+3 6.593000000000000e-3 3.192000000000000e+3 6.415000000000000e-3 3.188000000000000e+3 6.205400000000000e-3 3.184000000000000e+3 6.030500000000000e-3 3.180000000000000e+3 5.857000000000000e-3 3.176000000000000e+3 5.684900000000000e-3 3.172000000000000e+3 5.547400000000000e-3 3.168000000000000e+3 5.377800000000000e-3 3.164000000000000e+3 5.242700000000000e-3 3.160000000000000e+3 5.105700000000000e-3 3.156000000000000e+3 4.973799999999999e-3 3.152000000000000e+3 4.847500000000000e-3 3.148000000000000e+3 4.726500000000000e-3 3.144000000000000e+3 4.610300000000000e-3 3.140000000000000e+3 4.498900000000000e-3 3.136000000000000e+3 4.392000000000000e-3 3.132000000000000e+3 4.289200000000000e-3 3.128000000000000e+3 4.190400000000000e-3 3.124000000000000e+3 4.095400000000000e-3 3.120000000000000e+3 4.004000000000000e-3 3.116000000000000e+3 3.916000000000000e-3 3.112000000000000e+3 3.831200000000000e-3 3.108000000000000e+3 3.749600000000000e-3 3.104000000000000e+3 3.670800000000000e-3 3.100000000000000e+3 3.594900000000000e-3 3.096000000000000e+3 3.521600000000000e-3 3.092000000000000e+3 3.450900000000000e-3 3.088000000000000e+3 3.382500000000000e-3 3.084000000000000e+3 3.316500000000000e-3 3.080000000000000e+3 3.252800000000000e-3 3.076000000000000e+3 3.191100000000000e-3 3.072000000000000e+3 3.131500000000000e-3 3.068000000000000e+3 3.073800000000000e-3 3.064000000000000e+3 3.018000000000000e-3 3.060000000000000e+3 2.964000000000000e-3 3.056000000000000e+3 2.911600000000000e-3 3.052000000000000e+3 2.860900000000000e-3 3.048000000000000e+3 2.811800000000000e-3 3.044000000000000e+3 2.764100000000000e-3 3.040000000000000e+3 2.718000000000000e-3 3.036000000000000e+3 2.673200000000000e-3 3.032000000000000e+3 2.629700000000000e-3 3.028000000000000e+3 2.587500000000000e-3 3.024000000000000e+3 2.546600000000000e-3 3.020000000000000e+3 2.506900000000000e-3 3.016000000000000e+3 2.468300000000000e-3 3.012000000000000e+3 2.430800000000000e-3 3.008000000000000e+3 2.394400000000000e-3 3.004000000000000e+3 2.359000000000000e-3 3.000000000000000e+3 2.324600000000000e-3 2.996000000000000e+3 2.291100000000000e-3 2.992000000000000e+3 2.258500000000000e-3 2.988000000000000e+3 2.226900000000000e-3 2.984000000000000e+3 2.196100000000000e-3 2.980000000000000e+3 2.166200000000000e-3 2.976000000000000e+3 2.137000000000000e-3 2.972000000000000e+3 2.108600000000000e-3 2.968000000000000e+3 2.081000000000000e-3 2.964000000000000e+3 2.054100000000000e-3 2.960000000000000e+3 2.027900000000000e-3 2.956000000000000e+3 2.002400000000000e-3 2.952000000000000e+3 1.977500000000000e-3 2.948000000000000e+3 1.953200000000000e-3 2.944000000000000e+3 1.929600000000000e-3 2.940000000000000e+3 1.906600000000000e-3 2.936000000000000e+3 1.884100000000000e-3 2.932000000000000e+3 1.862300000000000e-3 2.928000000000000e+3 1.840900000000000e-3 2.924000000000000e+3 1.820100000000000e-3 2.920000000000000e+3 1.799800000000000e-3 2.916000000000000e+3 1.780000100000000e-3 2.912000000000000e+3 1.760700000000000e-3 2.908000000000000e+3 1.741900000000000e-3 2.904000000000000e+3 1.723500000000000e-3 2.900000000000000e+3 1.705500000000000e-3 2.896000000000000e+3 1.688000000000000e-3 2.892000000000000e+3 1.670900000000000e-3 2.888000000000000e+3 1.654200000000000e-3 2.884000000000000e+3 1.637900000000000e-3 2.880000000000000e+3 1.622000000000000e-3 2.876000000000000e+3 1.606500000000000e-3 2.872000000000000e+3 1.591300000000000e-3 2.868000000000000e+3 1.576500000000000e-3 2.864000000000000e+3 1.562000000000000e-3 2.860000000000000e+3 1.547900000000000e-3 2.856000000000000e+3 1.534100000000000e-3 2.852000000000000e+3 1.520600000000000e-3 2.848000000000000e+3 1.507400000000000e-3 2.844000000000000e+3 1.494600000000000e-3 2.840000000000000e+3 1.482000000000000e-3 2.836000000000000e+3 1.469700000000000e-3 2.832000000000000e+3 1.457700000000000e-3 2.828000000000000e+3 1.446000000000000e-3 2.824000000000000e+3 1.434500000000000e-3 2.820000000000000e+3 1.423300000000000e-3 2.816000000000000e+3 1.412400000000000e-3 2.812000000000000e+3 1.401700000000000e-3 2.808000000000000e+3 1.391300000000000e-3 2.804000000000000e+3 1.381100000000000e-3 2.800000000000000e+3 1.371100000000000e-3 2.796000000000000e+3 1.361400000000000e-3 2.792000000000000e+3 1.351900000000000e-3 2.788000000000000e+3 1.342600000000000e-3 2.784000000000000e+3 1.333500000000000e-3 2.780000000000000e+3 1.324600000000000e-3 2.776000000000000e+3 1.315900000000000e-3 2.772000000000000e+3 1.307500000000000e-3 2.768000000000000e+3 1.299200000000000e-3 2.764000000000000e+3 1.291100000000000e-3 2.760000000000000e+3 1.283200000000000e-3 2.756000000000000e+3 1.275500000000000e-3 2.752000000000000e+3 1.268000000000000e-3 2.748000000000000e+3 1.260600000000000e-3 2.744000000000000e+3 1.253400000000000e-3 2.740000000000000e+3 1.246400000000000e-3 2.736000000000000e+3 1.239600000000000e-3 2.732000000000000e+3 1.232900000000000e-3 2.728000000000000e+3 1.226400000000000e-3 2.724000000000000e+3 1.220000000000000e-3 2.720000000000000e+3 1.213800000000000e-3 2.716000000000000e+3 1.207800000000000e-3 2.712000000000000e+3 1.201900000000000e-3 2.708000000000000e+3 1.196100000000000e-3 2.704000000000000e+3 1.190500000000000e-3 2.700000000000000e+3 1.185000000000000e-3 2.696000000000000e+3 1.179700000000000e-3 2.692000000000000e+3 1.174400000000000e-3 2.688000000000000e+3 1.169400000000000e-3 2.684000000000000e+3 1.164400000000000e-3 2.680000000000000e+3 1.159600000000000e-3 2.676000000000000e+3 1.154900000000000e-3 2.672000000000000e+3 1.150400000000000e-3 2.668000000000000e+3 1.146000000000000e-3 2.664000000000000e+3 1.141600000000000e-3 2.660000000000000e+3 1.137400000000000e-3 2.656000000000000e+3 1.133300000000000e-3 2.652000000000000e+3 1.129400000000000e-3 2.648000000000000e+3 1.125500000000000e-3 2.644000000000000e+3 1.121800000000000e-3 2.640000000000000e+3 1.118200000000000e-3 2.636000000000000e+3 1.114700000000000e-3 2.632000000000000e+3 1.111200000000000e-3 2.628000000000000e+3 1.107900000000000e-3 2.624000000000000e+3 1.104700000000000e-3 2.620000000000000e+3 1.101600000000000e-3 2.616000000000000e+3 1.098600000000000e-3 2.612000000000000e+3 1.095700000000000e-3 2.608000000000000e+3 1.092900000000000e-3 2.604000000000000e+3 1.090200000000000e-3 2.600000000000000e+3 1.087600000000000e-3 2.596000000000000e+3 1.085100000000000e-3 2.592000000000000e+3 1.082700000000000e-3 2.588000000000000e+3 1.080400000000000e-3 2.584000000000000e+3 1.078100000000000e-3 2.580000000000000e+3 1.076000000000000e-3 2.576000000000000e+3 1.074000000000000e-3 2.572000000000000e+3 1.072000000000000e-3 2.568000000000000e+3 1.070100000000000e-3 2.564000000000000e+3 1.068300000000000e-3 2.560000000000000e+3 1.066600000000000e-3 2.556000000000000e+3 1.065000000000000e-3 2.552000000000000e+3 1.063500000000000e-3 2.548000000000000e+3 1.062000000000000e-3 2.544000000000000e+3 1.060700000000000e-3 2.540000000000000e+3 1.059400000000000e-3 2.536000000000000e+3 1.058200000000000e-3 2.532000000000000e+3 1.057100000000000e-3 2.528000000000000e+3 1.056000000000000e-3 2.524000000000000e+3 1.055100000000000e-3 2.520000000000000e+3 1.054200000000000e-3 2.516000000000000e+3 1.053400000000000e-3 2.512000000000000e+3 1.052600000000000e-3 2.508000000000000e+3 1.052000000000000e-3 2.504000000000000e+3 1.051400000000000e-3 2.500000000000000e+3 1.050900000000000e-3 2.496000000000000e+3 1.050500000000000e-3 2.492000000000000e+3 1.050200000000000e-3 2.488000000000000e+3 1.049900000000000e-3 2.484000000000000e+3 1.049700000000000e-3 2.480000000000000e+3 1.049600000000000e-3 2.476000000000000e+3 1.049500000000000e-3 2.472000000000000e+3 1.049500000000000e-3 2.468000000000000e+3 1.049600000000000e-3 2.464000000000000e+3 1.049800000000000e-3 2.460000000000000e+3 1.050000000000000e-3 2.456000000000000e+3 1.050300000000000e-3 2.452000000000000e+3 1.050700000000000e-3 2.448000000000000e+3 1.051200000000000e-3 2.444000000000000e+3 1.051700000000000e-3 2.440000000000000e+3 1.052300000000000e-3 2.436000000000000e+3 1.052900000000000e-3 2.432000000000000e+3 1.053700000000000e-3 2.428000000000000e+3 1.054500000000000e-3 2.424000000000000e+3 1.055300000000000e-3 2.420000000000000e+3 1.056300000000000e-3 2.416000000000000e+3 1.057300000000000e-3 2.412000000000000e+3 1.058400000000000e-3 2.408000000000000e+3 1.059500000000000e-3 2.404000000000000e+3 1.060700000000000e-3 2.400000000000000e+3 1.062000000000000e-3 2.396000000000000e+3 1.063400000000000e-3 2.392000000000000e+3 1.064800000000000e-3 2.388000000000000e+3 1.066300000000000e-3 2.384000000000000e+3 1.067900000000000e-3 2.380000000000000e+3 1.069600000000000e-3 2.376000000000000e+3 1.071300000000000e-3 2.372000000000000e+3 1.073000000000000e-3 2.368000000000000e+3 1.074900000000000e-3 2.364000000000000e+3 1.076800000000000e-3 2.360000000000000e+3 1.078700000000000e-3 2.356000000000000e+3 1.080800000000000e-3 2.352000000000000e+3 1.083000000000000e-3 2.348000000000000e+3 1.085200000000000e-3 2.344000000000000e+3 1.087400000000000e-3 2.340000000000000e+3 1.089800000000000e-3 2.336000000000000e+3 1.092200000000000e-3 2.332000000000000e+3 1.094700000000000e-3 2.328000000000000e+3 1.097200000000000e-3 2.324000000000000e+3 1.099800000000000e-3 2.320000000000000e+3 1.102600000000000e-3 2.316000000000000e+3 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