Energy Conversion Factors
| 1 kcal/mol |
|---|
| 0.04336 eV |
| 0.00159 h |
| 349.75 cm$^{-1}$ |
| 6.948 × 10$^{-14}$ erg |
| 4.184 kJ/mol |
| 1 eV |
|---|
| 23.06 kcal/mol |
| 0.03675 h |
| 8065.6 cm$^{-1}$ |
| 1.602 × 10$^{-12}$ erg |
| 1 h |
|---|
| 627.51 kcal/mol |
| 27.212 eV |
| 219,474.6 cm$^{-1}$ |
| 4.36 × 10$^{-11}$ erg |
| 2 Ry |
| 1 erg |
|---|
| 1.439 × 10$^{13}$ kcal/mol |
| 6.2415 × 10$^{11}$ eV |
| 2.2937 × 10$^{10}$ h |
| 5.034 × 10$^{15}$ cm$^{-1}$ |
Colors of Light
Visible Light
| Color | nm | eV | $\text{cm}^{-1}$ |
|---|---|---|---|
| Red | 700 | 1.77 | 14,300 |
| Orange | 620 | 2.00 | 16,100 |
| Yellow | 580 | 2.14 | 17,300 |
| Green | 530 | 2.34 | 18,900 |
| Blue | 470 | 2.64 | 21,300 |
| Violet | 420 | 2.95 | 23,800 |
All Light
| Color | nm | eV | $\text{cm}^{-1}$ |
|---|---|---|---|
| Radio | $3\times 10^{12}$ — $3\times 10^{8}$ | $4\times 10^{-10}$ — $4\times 10^{-6}$ | $3\times 10^{-6}$ — $3\times 10^{-2}$ |
| Microwaves | $3\times 10^{8}$ — $3\times 10^{6}$ | $4\times 10^{-6}$ — $4\times 10^{-4}$ | $3\times 10^{-2}$ — $3$ |
| Far IR | $3\times 10^{6}$ — $3\times 10^{4}$ | $4\times 10^{-4}$ — $4\times 10^{-2}$ | $3$ — $300$ |
| Near IR | $3\times 10^{4}$ — $700$ | $4\times 10^{-2}$ — $2$ | $300$ — $15,000$ |
| Visible | $700$ — $420$ | $2$ — $3$ | $15,000$ — $24,000$ |
| Near UV | $420$ — $300$ | $3$ — $4$ | $24,000$ — $30,000$ |
| Vac UV | $300$ — $3$ | $4$ — $400$ | $30,000$ — 3\e{6} |
| X-rays | $3$ — $0.003$ | $400$ — $4\times 10^{5}$ | $3\times 10^{6}$ — $3\times 10^{9}$ |
Free Energies
$$ \Delta(G) = RT \ln(K) $$ $$ \Delta(G_1) - \Delta(G_2) = RT\ln\left(\frac{K_1}{K_2}\right) $$ $$ \Delta\Delta(G) = 1\text{ kcal/mol} \Longleftrightarrow \frac{K_1}{K_2} = 5.4 $$ $$ \frac{K_1}{K_2} = 10^1 \Longleftrightarrow \Delta\Delta G = 1.36 $$ $$ \frac{K_1}{K_2} = 10^2 \Longleftrightarrow \Delta\Delta G = 2.76 $$ $$ \frac{K_1}{K_2} = 10^4 \Longleftrightarrow \Delta\Delta G = 5.53 $$ $$ \frac{K_1}{K_2} = 10^6 \Longleftrightarrow \Delta\Delta G = 8.29 $$ $$ \Delta G = 1.36 \left( pK_{a1} - pK_{a2}\right) $$
Atomic Units
| Length | Bohr radius, $a_0$ | 0.52918 Å |
|---|---|---|
| Force Constant | 1 au | $1.5569 \times 10^6$ dyn/cm |
| Mass | au, m$_\text{e}$ | $9.1095\times 10^{-31}$ kg |
| $5.5\times 10^{-4}$ amu | ||
| amu, m($^{12}$C)/12 | $1.66\times 10^{-27}$ kg | |
| 1822 au | ||
| Time | au | $2.4189\times 10^{-17}$ s |
| Dipole Moment | au | 2.54 D |
| $8.478\times 10^{-30}$ C-m |
Miscellaneous
Force Constants
$$ 1\text{ dyn/cm} = 1.44 \times 10^{-3}\frac{\text{ kcal/mol}}{\text{Å}^2} $$ $$ 1\text{ Mdyn/cm} = 1440\frac{\text{ kcal/mol}}{\text{Å}^2} $$
Thermal
$$ k_BT (298\text{ K}) = 9.4366 \times 10^{-4}\text{ h} $$ $$ RT (298\text{ K}) = 2.4789\text{ kJ/mol} = 0.5925\text{ kcal/mol} $$ $$ e^2 = 14.3998\text{ eV-Å} = 332.059\text{ (kcal/mol)-Å} $$
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