Results for Point Group D7h



Characters of representations for molecular motions
Motion E 2C7 2(C7)2 2(C7)3 7C'2 σh 2S7 2(S7)5 2(S7)3 7σv
Cartesian 3N 378 0.000 0.000 -0.000 0 28 0.000 -0.000 -0.000 10
Translation (x,y,z) 3 2.247 0.555 -0.802 -1 1 0.247 -1.445 -2.802 1
Rotation (Rx,Ry,Rz) 3 2.247 0.555 -0.802 -1 -1 -0.247 1.445 2.802 -1
Vibration 372 -4.494 -1.110 1.604 2 28 0.000 -0.000 -0.000 10


Decomposition to irreducible representations
Motion A'1 A'2 E'1 E'2 E'3 A''1 A''2 E''1 E''2 E''3 Total
Cartesian 3N 17 12 29 29 29 10 15 25 25 25 216
Translation (x,y,z) 0 0 1 0 0 0 1 0 0 0 2
Rotation (Rx,Ry,Rz) 0 1 0 0 0 0 0 1 0 0 2
Vibration 17 11 28 29 29 10 14 24 25 25 212



Molecular parameter
Number of Atoms (N) 126
Number of internal coordinates 372
Number of independant internal coordinates 17
Number of vibrational modes 212

Force field analysis


Allowed / forbidden vibronational transitions
Operator A'1 A'2 E'1 E'2 E'3 A''1 A''2 E''1 E''2 E''3 Total
Linear (IR) 17 11 28 29 29 10 14 24 25 25 42 / 170
Quadratic (Raman) 17 11 28 29 29 10 14 24 25 25 70 / 142
IR + Raman - - - - 11 - - - - - - - - 29 10 - - - - - - - - 25 25 0 / 100


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C7 2(C7)2 2(C7)3 7C'2 σh 2S7 2(S7)5 2(S7)3 7σv
linear 372 -4.494 -1.110 1.604 2 28 0.000 -0.000 -0.000 10
quadratic 69.378 9.543 1.418 -0.961 188 578 -0.555 0.802 -2.247 236
cubic 8.649.124 -12.098 -2.616 -3.286 374 8.876 -0.000 -0.000 0.000 2.030
quartic 810.855.375 9.543 1.418 -0.961 17.765 116.175 0.555 -0.802 2.247 27.141
quintic 60.976.324.200 -4.494 -1.110 1.604 35.156 1.316.280 0.000 0.000 0.000 206.532
sextic 3.831.345.703.900 1.000 1.000 1.000 1.124.992 13.422.940 -1.000 -1.000 -1.000 2.045.056


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A'1 A'2 E'1 E'2 E'3 A''1 A''2 E''1 E''2 E''3
linear 17 11 28 29 29 10 14 24 25 25
quadratic 2.605 2.393 4.998 4.996 4.996 2.446 2.470 4.915 4.914 4.913
cubic 309.814 308.612 618.428 618.429 618.430 308.165 308.993 617.160 617.161 617.162
quartic 28.974.497 28.952.044 57.926.540 57.926.539 57.926.538 28.952.628 28.957.316 57.909.944 57.909.942 57.909.942
quintic 2.177.833.296 2.177.712.452 4.355.545.748 4.355.545.749 4.355.545.749 2.177.636.010 2.177.721.698 4.355.357.708 4.355.357.709 4.355.357.709
sextic 136.835.047.042 136.833.462.018 273.668.509.060 273.668.509.060 273.668.509.060 136.833.065.733 136.833.525.765 273.666.591.497 273.666.591.497 273.666.591.497


Further Reading


Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of D7h

Subtotal: <Number of nonvanishing force constants in subsection> / <number of nonzero irrep combinations in subsection> / <number of irrep combinations in subsection>
Total: <Number of nonvanishing force constants in force field> / <number of nonzero irrep combinations in force field> / <number of irrep combinations in force field>


Contributions to nonvanishing quadratic force field constants
Irrep combinations (i,i) with indices: pos(A'1) ≤ i ≤ pos(E''3)
..153. A'1A'1...66. A'2A'2...406. E'1E'1...435. E'2E'2...435. E'3E'3...55. A''1A''1...105. A''2A''2...300. E''1E''1...325. E''2E''2...325. E''3E''3.
Subtotal: 2.605 / 10 / 10
Irrep combinations (i,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E''3)
Subtotal: 0 / 0 / 45
Total: 2.605 / 10 / 55


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A'1) ≤ i ≤ pos(E''3)
..969. A'1A'1A'1.
Subtotal: 969 / 1 / 10
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E''3)
..11.774. E'1E'1E'2...12.615. E'2E'2E'3...1.122. A'1A'2A'2...6.902. A'1E'1E'1...7.395. A'1E'2E'2...7.395. A'1E'3E'3...935. A'1A''1A''1...1.785. A'1A''2A''2...5.100. A'1E''1E''1...5.525. A'1E''2E''2.
..5.525. A'1E''3E''3...4.158. A'2E'1E'1...4.466. A'2E'2E'2...4.466. A'2E'3E'3...3.036. A'2E''1E''1...3.300. A'2E''2E''2...3.300. A'2E''3E''3...12.180. E'1E'3E'3...9.100. E'1E''3E''3...8.700. E'2E''1E''1.
..9.425. E'3E''2E''2.
Subtotal: 128.204 / 21 / 90
Irrep combinations (i,j,k) with indices: pos(A'1) ≤ i ≤ j ≤ k ≤ pos(E''3)
..1.540. A'2A''1A''2...23.548. E'1E'2E'3...6.720. E'1A''1E''1...9.408. E'1A''2E''1...16.800. E'1E''1E''2...17.500. E'1E''2E''3...7.250. E'2A''1E''2...10.150. E'2A''2E''2...17.400. E'2E''1E''3...18.125. E'2E''2E''3.
..7.250. E'3A''1E''3...10.150. E'3A''2E''3...17.400. E'3E''1E''2...17.400. E'3E''1E''3.
Subtotal: 180.641 / 14 / 120
Total: 309.814 / 36 / 220


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A'1) ≤ i ≤ pos(E''3)
..4.845. A'1A'1A'1A'1...1.001. A'2A'2A'2A'2...82.621. E'1E'1E'1E'1...94.830. E'2E'2E'2E'2...94.830. E'3E'3E'3E'3...715. A''1A''1A''1A''1...2.380. A''2A''2A''2A''2...45.150. E''1E''1E''1E''1...52.975. E''2E''2E''2E''2...52.975. E''3E''3E''3E''3.
Subtotal: 432.322 / 10 / 10
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E''3)
..117.740. E'1E'1E'1E'3...65.000. E''1E''1E''1E''3...125.860. E'1E'2E'2E'2...130.355. E'2E'3E'3E'3...70.200. E''1E''2E''2E''2...73.125. E''2E''3E''3E''3.
Subtotal: 582.280 / 6 / 90
Irrep combinations (i,i,j,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E''3)
..10.098. A'1A'1A'2A'2...62.118. A'1A'1E'1E'1...66.555. A'1A'1E'2E'2...66.555. A'1A'1E'3E'3...8.415. A'1A'1A''1A''1...16.065. A'1A'1A''2A''2...45.900. A'1A'1E''1E''1...49.725. A'1A'1E''2E''2...49.725. A'1A'1E''3E''3...26.796. A'2A'2E'1E'1.
..28.710. A'2A'2E'2E'2...28.710. A'2A'2E'3E'3...3.630. A'2A'2A''1A''1...6.930. A'2A'2A''2A''2...19.800. A'2A'2E''1E''1...21.450. A'2A'2E''2E''2...21.450. A'2A'2E''3E''3...330.078. E'1E'1E'2E'2...330.078. E'1E'1E'3E'3...22.330. E'1E'1A''1A''1.
..42.630. E'1E'1A''2A''2...347.928. E'1E'1E''1E''1...245.350. E'1E'1E''2E''2...245.350. E'1E'1E''3E''3...354.061. E'2E'2E'3E'3...23.925. E'2E'2A''1A''1...45.675. E'2E'2A''2A''2...242.556. E'2E'2E''1E''1...404.550. E'2E'2E''2E''2...263.175. E'2E'2E''3E''3.
..23.925. E'3E'3A''1A''1...45.675. E'3E'3A''2A''2...242.556. E'3E'3E''1E''1...263.175. E'3E'3E''2E''2...404.550. E'3E'3E''3E''3...5.775. A''1A''1A''2A''2...16.500. A''1A''1E''1E''1...17.875. A''1A''1E''2E''2...17.875. A''1A''1E''3E''3...31.500. A''2A''2E''1E''1.
..34.125. A''2A''2E''2E''2...34.125. A''2A''2E''3E''3...180.300. E''1E''1E''2E''2...180.300. E''1E''1E''3E''3...195.625. E''2E''2E''3E''3.
Subtotal: 5.124.199 / 45 / 45
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A'1) ≤ i ≤ j ≤ k ≤ pos(E''3)
..341.446. E'1E'1E'2E'3...52.920. E'1E'1A''1A''2...101.500. E'1E'1A''1E''2...142.100. E'1E'1A''2E''2...243.600. E'1E'1E''1E''3...253.750. E'1E'1E''2E''3...56.840. E'2E'2A''1A''2...108.750. E'2E'2A''1E''3...152.250. E'2E'2A''2E''3...261.000. E'2E'2E''1E''2.
..261.000. E'2E'2E''1E''3...56.840. E'3E'3A''1A''2...104.400. E'3E'3A''1E''1...146.160. E'3E'3A''2E''1...261.000. E'3E'3E''1E''2...271.875. E'3E'3E''2E''3...187.500. E''1E''1E''2E''3...200.158. A'1E'1E'1E'2...214.455. A'1E'2E'2E'3...129.514. A'2E'1E'1E'2.
..138.765. A'2E'2E'2E'3...353.220. E'1E'2E'2E'3...75.000. A''1E''1E''1E''2...81.250. A''1E''2E''2E''3...105.000. A''2E''1E''1E''2...113.750. A''2E''2E''2E''3...195.000. E''1E''2E''2E''3...70.686. A'1A'2E'1E'1...75.922. A'1A'2E'2E'2...75.922. A'1A'2E'3E'3.
..51.612. A'1A'2E''1E''1...56.100. A'1A'2E''2E''2...56.100. A'1A'2E''3E''3...207.060. A'1E'1E'3E'3...154.700. A'1E'1E''3E''3...147.900. A'1E'2E''1E''1...160.225. A'1E'3E''2E''2...133.980. A'2E'1E'3E'3...100.100. A'2E'1E''3E''3...95.700. A'2E'2E''1E''1.
..103.675. A'2E'3E''2E''2...353.220. E'1E'2E'3E'3...263.900. E'1E'2E''2E''2...263.900. E'1E'2E''3E''3...243.600. E'1E'3E''1E''1...263.900. E'1E'3E''2E''2...252.300. E'2E'3E''1E''1...273.325. E'2E'3E''3E''3...38.640. A''1A''2E''1E''1...42.000. A''1A''2E''2E''2.
..42.000. A''1A''2E''3E''3...78.000. A''1E''1E''3E''3...109.200. A''2E''1E''3E''3...195.000. E''1E''2E''3E''3.
Subtotal: 8.517.710 / 54 / 360
Irrep combinations (i,j,k,l) with indices: pos(A'1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E''3)
..26.180. A'1A'2A''1A''2...400.316. A'1E'1E'2E'3...114.240. A'1E'1A''1E''1...159.936. A'1E'1A''2E''1...285.600. A'1E'1E''1E''2...297.500. A'1E'1E''2E''3...123.250. A'1E'2A''1E''2...172.550. A'1E'2A''2E''2...295.800. A'1E'2E''1E''3...308.125. A'1E'2E''2E''3.
..123.250. A'1E'3A''1E''3...172.550. A'1E'3A''2E''3...295.800. A'1E'3E''1E''2...295.800. A'1E'3E''1E''3...259.028. A'2E'1E'2E'3...73.920. A'2E'1A''1E''1...103.488. A'2E'1A''2E''1...184.800. A'2E'1E''1E''2...192.500. A'2E'1E''2E''3...79.750. A'2E'2A''1E''2.
..111.650. A'2E'2A''2E''2...191.400. A'2E'2E''1E''3...199.375. A'2E'2E''2E''3...79.750. A'2E'3A''1E''3...111.650. A'2E'3A''2E''3...191.400. A'2E'3E''1E''2...191.400. A'2E'3E''1E''3...194.880. E'1E'2A''1E''1...203.000. E'1E'2A''1E''3...272.832. E'1E'2A''2E''1.
..284.200. E'1E'2A''2E''3...974.400. E'1E'2E''1E''2...487.200. E'1E'2E''1E''3...507.500. E'1E'2E''2E''3...203.000. E'1E'3A''1E''2...203.000. E'1E'3A''1E''3...284.200. E'1E'3A''2E''2...284.200. E'1E'3A''2E''3...487.200. E'1E'3E''1E''2...974.400. E'1E'3E''1E''3.
..507.500. E'1E'3E''2E''3...201.840. E'2E'3A''1E''1...210.250. E'2E'3A''1E''2...282.576. E'2E'3A''2E''1...294.350. E'2E'3A''2E''2...504.600. E'2E'3E''1E''2...504.600. E'2E'3E''1E''3...1.051.250. E'2E'3E''2E''3...150.000. A''1E''1E''2E''3...210.000. A''2E''1E''2E''3.
Subtotal: 14.317.986 / 50 / 210
Total: 28.974.497 / 165 / 715


Calculate contributions to

A'1 A'2 E'1 E'2 E'3 A''1 A''2 E''1 E''2 E''3
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Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement