Why calculate negative frequencies of DFT?

1. Why do we need negative frequency?
2. Why there is negative frequency in Fourier transform?
3. What do negative frequencies represent?
4. What does negative frequency mean in Gaussian?

Why do we need negative frequency?

In real world, the negative frequency does not exists and the spectral content on negative frequencies must be added to the spectral content at the positive frequencies, to save energy. The concept of negative frequencies is used broad wide namely in this sense, in the connection with complex numbers.

Why there is negative frequency in Fourier transform?

The reason is that the Fourier transform is symmetric about the y-axis, because the Fourier transform is mathematically defined on the interval (-Inf,Inf). The actual Fourier transform therefore has negative frequencies.

What do negative frequencies represent?

Remembering that physically, sinusoids are waves, the sign of the frequency represents the direction of wave propagation. Simply put, negative frequencies represent forward traveling waves, while positive frequencies represent backward traveling waves.

What does negative frequency mean in Gaussian?

Negative frequency or imaginary frequency suggests that your molecule is not minima on PES (Potential Energy Surface); instead, it's a transition state structure (one negative freq. refers to the first-order saddle point). You need to follow up on the negative frequency to get the equilibrium geometry.