The paper proposes a van der Waals density functional (vdW-DF) within density functional theory (DFT) to extend the method successfully applied to layered geometries to general geometries. The functional includes van der Waals forces by expanding the nonlocal correlation energy to second order in a carefully chosen quantity, which is expressed as a density-density interaction formula. The parameters of the parametrized kernel are determined by the local density and its gradient. The vdW-DF is applied to rare gas and benzene dimers, showing realistic descriptions. The authors derive the nonlocal correlation energy term and show its agreement with standard formulas for long-range interactions. They also discuss the numerical evaluation and the choice of the kernel function, which depends on a single length scale. The functional is compared with experimental data and other methods, demonstrating its promise for calculating properties of van der Waals-bound molecules.The paper proposes a van der Waals density functional (vdW-DF) within density functional theory (DFT) to extend the method successfully applied to layered geometries to general geometries. The functional includes van der Waals forces by expanding the nonlocal correlation energy to second order in a carefully chosen quantity, which is expressed as a density-density interaction formula. The parameters of the parametrized kernel are determined by the local density and its gradient. The vdW-DF is applied to rare gas and benzene dimers, showing realistic descriptions. The authors derive the nonlocal correlation energy term and show its agreement with standard formulas for long-range interactions. They also discuss the numerical evaluation and the choice of the kernel function, which depends on a single length scale. The functional is compared with experimental data and other methods, demonstrating its promise for calculating properties of van der Waals-bound molecules.