Table 2. Comparison of geometrical parameters of the four selected b-D-glucose conformers for X-ray crystal, MP2, DFT and HF structures.a
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| (1) 4C1 t t t t G+ g- |
| (2) 4C1 t t t t T g+ | |||||||||||
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| X-rayb | MP2c | B3LYP | B3LYP/+ | BP /+ | HF |
| MP2c | B3LYP | B3LYP/f | B3LYP/+ | BP/+ | HF | HF/+ |
Bond lengths |
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C1-C2 |
| 1.525 | 1.523 | 0.004 | 0.008 | 0.014 | -0.004 |
| 1.523 | 0.005 | 0.006 | 0.007 | 0.013 | -0.004 | -0.002 |
C2-C3 |
| 1.520 | 1.517 | 0.005 | 0.007 | 0.012 | 0.000 |
| 1.517 | 0.006 | 0.006 | 0.008 | 0.013 | 0.001 | 0.002 |
C3-C4 |
| 1.511 | 1.520 | 0.007 | 0.009 | 0.014 | 0.000 |
| 1.518 | 0.005 | 0.006 | 0.007 | 0.011 | 0.000 | 0.001 |
C4-C5 |
| 1.529 | 1.526 | 0.007 | 0.009 | 0.014 | -0.001 |
| 1.531 | 0.007 | 0.007 | 0.007 | 0.013 | -0.002 | -0.002 |
C5-C6 |
| 1.513 | 1.520 | 0.004 | 0.005 | 0.010 | -0.002 |
| 1.527 | 0.005 | 0.005 | 0.005 | 0.011 | -0.003 | -0.002 |
O5-C1 |
| 1.433 | 1.422 | 0.002 | 0.001 | 0.015 | -0.027 |
| 1.420 | 0.001 | 0.001 | 0.003 | 0.017 | -0.026 | -0.026 |
C1-O1 |
| 1.383 | 1.394 | 0.001 | 0.003 | 0.011 | -0.017 |
| 1.394 | 0.002 | 0.002 | 0.004 | 0.012 | -0.017 | -0.016 |
C2-O2 |
| 1.429 | 1.420 | 0.002 | 0.005 | 0.015 | -0.020 |
| 1.420 | 0.002 | 0.001 | 0.005 | 0.015 | -0.020 | -0.019 |
C3-O3 |
| 1.432 | 1.421 | 0.001 | 0.005 | 0.015 | -0.020 |
| 1.421 | 0.001 | 0.001 | 0.004 | 0.015 | -0.020 | -0.020 |
C4-O4 |
| 1.419 | 1.418 | 0.000 | 0.004 | 0.014 | -0.021 |
| 1.425 | 0.001 | 0.001 | 0.004 | 0.014 | -0.023 | -0.022 |
C5-O5 |
| 1.437 | 1.437 | 0.001 | 0.002 | 0.013 | -0.022 |
| 1.430 | 0.002 | 0.002 | 0.005 | 0.015 | -0.020 | -0.020 |
C6-O6 |
| 1.419 | 1.416 | 0.001 | 0.006 | 0.015 | -0.018 |
| 1.413 | 0.000 | 0.000 | 0.006 | 0.014 | -0.019 | -0.017 |
Mean error |
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|
| 0.003 | 0.005 | 0.014 | -0.013 |
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| 0.003 | 0.003 | 0.005 | 0.014 | -0.013 | -0.012 |
Valence angles |
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C5-O5-C1 |
| 112.7 | 111.3 | 2.0 | 2.1 | 1.2 | 3.4 |
| 111.2 | 1.9 | 1.8 | 2.0 | 1.1 | 3.4 | 3.3 |
O5-C1-O1 |
| 107.0 | 109.3 | -0.1 | -0.3 | -0.4 | 0.0 |
| 109.2 | -0.2 | 0.2 | -0.4 | -0.5 | 0.0 | -0.1 |
Dihedral angles |
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O5-C1-C2-C3 |
| 53.7 | 58.4 | -1.3 | -1.5 | -1.0 | -1.8 |
| 57.9 | -1.0 | -1.1 | -1.4 | -0.6 | -2.0 | -2.3 |
C1-C2-C3-C4 |
| -50.8 | -54.0 | -0.1 | 0.5 | 0.3 | 0.4 |
| -53.3 | -0.4 | -0.1 | -0.2 | -0.5 | 0.1 | 0.3 |
C2-C3-C4-C5 |
| 53.4 | 53.7 | 0.1 | -0.2 | 0.0 | -0.3 |
| 54.4 | 0.1 | 0.0 | 0.4 | 0.5 | 0.1 | 0.2 |
C3-C4-C5-O5 |
| -59.8 | -57.4 | 1.5 | 1.7 | 0.9 | 2.3 |
| -58.7 | 1.8 | 1.5 | 1.3 | 1.0 | 1.8 | 1.4 |
C4-C5-O5-C1 |
| 66.3 | 63.5 | -1.7 | -1.5 | -0.6 | -1.8 |
| 64.0 | -2.2 | -1.8 | -1.8 | -1.5 | -1.3 | -1.1 |
C5-O5-C1-C2 |
| -62.8 | -63.9 | 1.5 | 1.1 | 0.4 | 1.2 |
| -64.3 | 1.6 | 1.4 | 1.7 | 1.1 | 1.5 | 1.6 |
Mean absolute error |
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| 1.0 | 1.1 | 0.6 | 1.3 |
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| 1.2 | 1.0 | 1.1 | 0.9 | 1.1 | 1.1 |
Table 2. continued.
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| (3) 1C4 t g+ g-- g- G+ g+ |
| (4) 1C4 g-- g++ g-- g++ G- g- | ||||||||
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| MP2c | B3LYP | B3LYP/f | B3LYP/+ | BP | BP/+ |
| MP2c | B3LYP | B3LYP/+ | BP |
Bond lengths |
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C1-C2 |
| 1.531 | 0.006 | 0.006 | 0.006 | 0.014 | 0.014 |
| 1.532 | 0.005 | 0.015 | 0.013 |
C2-C3 |
| 1.541 | 0.005 | 0.005 | 0.004 | 0.011 | 0.010 |
| 1.536 | 0.004 | 0.004 | 0.010 |
C3-C4 |
| 1.544 | 0.006 | 0.006 | 0.006 | 0.014 | 0.014 |
| 1.539 | 0.003 | 0.002 | 0.010 |
C4-C5 |
| 1.533 | 0.006 | 0.006 | 0.007 | 0.010 | 0.011 |
| 1.549 | 0.005 | -0.001 | 0.011 |
C5-C6 |
| 1.549 | 0.008 | 0.007 | 0.008 | 0.015 | 0.017 |
| 1.528 | 0.004 | 0.009 | 0.009 |
O5-C1 |
| 1.422 | 0.000 | 0.000 | 0.003 | 0.015 | 0.010 |
| 1.419 | -0.003 | -0.005 | 0.010 |
C1-O1 |
| 1.419 | 0.003 | 0.003 | 0.007 | 0.015 | 0.019 |
| 1.410 | 0.004 | -0.007 | 0.014 |
C2-O2 |
| 1.413 | 0.000 | 0.000 | 0.004 | 0.008 | 0.013 |
| 1.432 | 0.003 | 0.004 | 0.014 |
C3-O3 |
| 1.419 | 0.000 | 0.000 | 0.004 | 0.008 | 0.012 |
| 1.432 | 0.002 | 0.004 | 0.014 |
C4-O4 |
| 1.435 | 0.001 | 0.002 | 0.005 | 0.012 | 0.015 |
| 1.421 | 0.001 | 0.001 | 0.008 |
C5-O5 |
| 1.433 | 0.000 | 0.001 | 0.000 | 0.012 | 0.012 |
| 1.454 | 0.002 | -0.012 | 0.015 |
C6-O6 |
| 1.427 | 0.001 | 0.001 | 0.001 | 0.014 | 0.013 |
| 1.426 | 0.001 | 0.002 | 0.011 |
Mean error |
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| 0.003 | 0.003 | 0.005 | 0.012 | 0.013 |
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| 0.003 | 0.001 | 0.012 |
Valence angles |
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C5-O5-C1 |
| 115.2 | 1.8 | 1.7 | 2.4 | 0.8 | 1.5 |
| 118.0 | 1.3 | 1.3 | 0.1 |
O5-C1-O1 |
| 112.2 | -0.3 | -0.3 | -0.5 | 0.0 | -0.2 |
| 115.6 | -0.4 | -0.9 | -0.1 |
Dihedral angles |
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O5-C1-C2-C3 |
| -57.8 | 1.2 | 1.2 | 2.2 | -0.4 | 0.7 |
| -62.3 | 1.7 | 13.4 | -0.2 |
C1-C2-C3-C4 |
| 53.4 | 0.5 | 0.2 | -1.0 | 1.7 | 0.4 |
| 59.6 | -0.6 | -11.2 | 0.5 |
C2-C3-C4-C5 |
| -49.6 | 0.0 | -0.1 | 1.5 | -0.6 | 0.6 |
| -47.3 | -0.1 | 0.3 | -0.7 |
C3-C4-C5-O5 |
| 48.2 | -2.0 | -1.5 | -3.4 | -1.6 | -2.9 |
| 38.4 | -0.6 | 7.6 | 0.2 |
C4-C5-O5-C1 |
| -53.0 | 2.7 | 2.1 | 3.6 | 2.8 | 3.7 |
| -43.1 | 1.0 | -5.8 | -0.2 |
C5-O5-C1-C2 |
| 58.5 | -2.3 | -2.0 | -2.9 | -1.9 | -2.6 |
| 54.1 | -1.2 | -4.3 | 0.3 |
Mean absolute error |
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| 1.4 | 1.2 | 2.4 | 1.5 | 1.8 |
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| 0.9 | 7.1 | 0.4 |
a The angles are in º, the distances are in Å. The first column for a conformer shows the value of the geometric parameter, the following columns contain the difference. /f denotes fine grid, /+ denotes diffuse functions added to the basis set. b Ref. 26. c Ref. 10.