FTIR Data

FTIRCalculationsRevised.pdf

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R P J 1/2(R(J)-P(J)) 2J+1 1/2(R(J)-P(J+2)) 2J+3 Value Unit Value Unit Value Unit Value Unit Term Value Unit

1330.6944 0 665.3472 1 3.5364 3 299792458 ms-1 Ref. NIST Atomic mass 1.66054E-27 kg 1 amu SB0H 2.83238E-04 cm-1

1333.0724 1325.9367 1 3.56785 3 5.8964 5 6.62607E-34 Js Ref. NIST Mass of H mh 1.67349E-27 kg 1.0078 amu SB1H 4.46591E-04 cm-1

1335.4676 1323.6216 2 5.923 5 8.24935 7 -0.00303 cm-1 Mass of D md 3.34449E-27 kg 2.0141 amu SB0H^2 8.02238E-08 cm-2

1337.8087 1321.2796 3 8.26455 7 10.591 9 1.17532 cm-1 117.53 m-1 Mass of C mc 1.99447E-26 kg 12.011 amu SB1H^2 1.99444E-07 cm-2

1340.2262 1318.9689 4 10.62865 9 12.95205 11 2.38171E-46 kgm2 2.3817E-39 gcm2 1/mh 5.97553E+26 1/kg SAH 5.28836E-04 cm-1

1342.6028 1316.6267 5 12.98805 11 15.30215 13 1/md 2.98999E+26 1/kg SAH^2 2.79667E-07 cm-2

1345.0112 1314.3221 6 15.34455 13 17.65465 15 1.1751 cm-1 117.51 m-1 1/mc 5.01385E+25 1/kg SbeH 3.87480E-04 cm-1

1347.3954 1311.9985 7 17.69845 15 20.01185 17 2.38051E-46 cm-1 SbeH^2 1.50141E-07 cm-2

1349.7762 1309.7019 8 20.03715 17 22.33885 19

1352.1886 1307.3717 9 22.40845 19 SB0D 1.03358E-03 cm-1

1305.0985 10 -652.54925 1.17987 0 Inertia of C2H2 Ih 2.38171E-46 kgm2 SB1D 8.96431E-04 cm-1

0.00044659 #N/A Inertia of C2D2 Id 3.30284E-46 kgm2 SB0D^2 1.06829E-06 cm-2

1.00000 0.02 SB1D^2 8.03589E-07 cm-1

6979865 8 C-C distance rcc 1.20965E-10 m 1.20965 A SAD 1.36817E-03 cm-1

1850 0.0 C-H distance rch 1.05536E-10 m 1.05536 A SAD^2 1.87188E-06 cm-1

SbeD 1.23946E-03 cm-1

SbeD^2 1.53626E-06 cm-2

1.17684 0 Inertia of C2H2 Tih 2.38051E-46 kgm2

0.00028324 #N/A Inertia of C2D2 Tid 3.30733E-46 kgm2 dIh/dBh -2.02644E-48

1.00000 0.01032557 dId/dBd -3.89700E-48

17263499 8 C-C distance Trcc 1.20679E-10 m 1.2068 A SIH 7.85203E-52 kgm2

1841 0.00085294 C-H distance Trch 1.06191E-10 m 1.06191 A SIH^2 6.16544E-103 kg2m4

SID 4.83018E-51 kgm2

SID^2 2.33306E-101 kg2m4

R P J 1/2(R(J)-P(J)) 2J+1 1/2(R(J)-P(J+2)) 2J+3 Value Unit Value Unit C2H2 C2D2 1043.2810 0 521.6405 1 2.51045 3 299792458 ms-1 Ref. NIST Const. Unit Value Error Value Error drc/dId -4.15106E+35

1044.9781 1039.9516 1 2.51325 3 4.23955 5 6.62607E-34 Js Ref. NIST B1 cm-1 1.1799 0.0004 0.8540 0.0009 (drc/dId)^2 1.72313E+71

1046.7127 1038.2601 2 4.2263 5 5.91175 7 -0.00429 cm-1 B0 cm-1 1.1768 0.0003 0.8497 0.0010 SID^2*(drc/dId)^2 4.02016E-30

1048.4536 1036.4990 3 5.9773 7 7.6512 9 0.84754 cm-1 84.754 m-1 ae cm-1 -0.0030 0.0005 -0.0043 0.0014 drc/dIh 8.29594E+35

1050.2003 1034.8892 4 7.65555 9 9.33805 11 3.30284E-46 kgm2 3.3028E-39 gcm2 Be cm-1 1.1753 0.0004 0.8475 0.0012 (drc/dIh)^2 6.88226E+71

1051.9530 1033.1512 5 9.4009 11 11.1038 13 Ie kgm2 2.38171E-46 7.9E-52 3.30284E-46 4.8E-51 SIH^2*(drc/dIh)^2 4.24322E-31

1053.6753 1031.5242 6 11.07555 13 12.743 15 0.84604 cm-1 84.604 m-1 Ie gcm2 2.38171E-39 7.9E-45 3.30284E-39 4.8E-44

1055.4190 1029.7454 7 12.8368 15 14.49035 17 3.30639E-46 cm-1 drh/dId 9.01169E+35

1057.1915 1028.1893 8 14.5011 17 16.08965 19 rcc A 1.20965 0.00002 (drh/dId)^2 8.12106E+71

1058.9698 1026.4383 9 16.26575 19 rch A 1.05536 0.00005 SID^2*(drh/dId)^2 1.89469E-29

1025.0122 10 -512.5061 0.85397 0 drh/dIh -9.01169E+35

0.000896 #N/A (drh/dIh)^2 8.12106E+71

0.99999 0.03 SIH^2*(drh/dIh)^2 5.00699E-31

907506 8 drh/drc -5.00000E-01

969 0.01 (drh/drc)^2 2.50000E-01

SRC^2*(drh/drc)^2 1.11112E-30

0.84968 0

0.0010336 #N/A SRC 2.10819E-15 m

0.99999 0.04 SRC^2 4.44448E-30 m2

675803 8 SRH 4.53417E-15 m

959 0.01 SRH^2 2.05587E-29 m2

Spring 2020

Error Propagation

Data Summary

Table values

Calculated values

Calculation Sheet for Molecular Spectroscopy of Acetylene

Slope, m (B1)

r2 of B1 curve

Const.

ae=

Be=

Ie=

Tbe=

Table values

Const.

Bond length calculation

Tie=

ssreg

Intercept of B1 Curve, b

r2 of B0 curve

Slope, m (B0) Intercept of B0 Curve, b

C2H2

C2D2

Tbe=

sm sb

Slope, m (B1) Intercept of B1 Curve, b

Const.

ae=

Be=

Ie=

Table values

r2 of B1 curve sy

Tie=

ssresid

ssreg

Slope, m (B0)

r2 of B0 curve

Intercept of B0 Curve, b

y = 1.1799x R² = 1

0 5 10 15 20

1 /2

(R (J

)- P

(J +1

))

2J+1

y = 1.1768x R² = 1

0 5 10 15 20

1 /2

(R (J

)- P

(J +2

))

2J+3

y = 0.854x R² = 1

0 5 10 15 20

1 /2

(R (J

)- P

(J +1

))

2J+1

y = 0.8497x R² = 0.9999

0 5 10 15 20

1 /2

(R (J

)- P

(J +2

))

2J+3

 Partial derivatives for error propagation

 𝜎𝛼𝑒 2 = (

𝜕𝛼𝑒

𝜕𝐵0 )2𝜎𝐵0

2 + ( 𝜕𝛼𝑒

𝜕𝐵1 )2𝜎𝐵1

 𝜎𝐵𝑒 2 = (

𝜕𝐵𝑒

𝜕𝐵0 )2𝜎𝐵0

2 + ( 𝜕𝐵𝑒

𝜕𝛼𝑒 )2𝜎𝛼𝑒

2 or 𝜎𝐵𝑒 2 = (

𝜕𝐵𝑒

𝜕𝐵1 )2𝜎𝐵1

2 + ( 𝜕𝐵𝑒

𝜕𝛼𝑒 )2𝜎𝛼𝑒

 𝜎𝐼𝑒 2 = (

𝜕𝐼𝑒

𝜕𝐵𝑒 )2𝜎𝐵𝑒

 𝜎𝑟𝐶𝐶 2 = (

𝜕𝑟𝐶𝐶

𝜕𝐼𝑒,𝐻 )2𝜎𝐼𝑒,𝐻

2 + ( 𝜕𝑟𝐶𝐶

𝜕𝐼𝑒,𝐷 )2𝜎𝐼𝑒,𝐷

 𝜎𝑟𝐶𝐻 2 = (

𝜕𝑟𝐶𝐻

𝜕𝐼𝑒,𝐻 )2𝜎𝐼𝑒,𝐻

2 + ( 𝜕𝑟𝐶𝐻

𝜕𝐼𝑒,𝐷 )2𝜎𝐼𝑒,𝐷

2 + ( 𝜕𝑟𝐶𝐻

𝜕𝑟𝐶𝐶 )2𝜎𝑟𝐶𝐶