A new nonempirical generalized gradient approximation (GGA) for density functional theory (DFT) is introduced, which significantly improves the accuracy of lattice constants, crystal structures, and metal surface energies compared to the popular Perdew-Burke-Ernzerhof (PBE) GGA. The new functional is based on a diffuse radial cutoff for the exchange hole in real space and an analytic gradient expansion of the exchange energy for small gradients. It has no adjustable parameters and maintains the constraining conditions of PBE, making it easy to implement in existing codes. The Kohn-Sham DFT allows efficient and accurate calculation of many-electron ground-state problems. However, the exchange-correlation (XC) energy is not known exactly, so approximations are needed. Local density approximation (LDA) and generalized gradient approximations (GGAs) are used, with GGAs improving upon LDA. However, GGAs often overcorrect LDA for solids, leading to inaccurate lattice constants. LSD underestimates the equilibrium lattice constant, while GGAs tend to overestimate it. The new functional addresses these issues by using a diffuse radial cutoff, which results in a smaller exchange enhancement factor $ F_X $ for larger gradients. The new functional, referred to as "WC," is derived from the PBE functional but incorporates a revised form of $ F_X $ that satisfies known constraints and improves accuracy for solids. It performs well for solids, with significant improvements in lattice constants, bulk moduli, and cohesive energies compared to LSD and PBE. For ferroelectrics like $ PbTiO_3 $, WC predicts more accurate volumes and strains than PBE. The new functional also performs better than PBE for jellium surface energies and is more accurate for noble-gas atoms than LSD and PBE. The WC functional is nonempirical, with no adjustable parameters, and is suitable for ab initio calculations of materials requiring high accuracy, such as ferroelectrics. It can be generalized to improve accuracy for atoms, molecules, and solids compared to PBE. The study shows that the accuracy of GGAs depends on the variation of the reduced gradient $ s $ and the density parameter $ r_s $, suggesting that a GGA with $ F_X $ depending on both $ s $ and $ r_s $ could be more accurate than PBE. The new functional represents a significant improvement over existing GGAs and meta-GGAs for solids.A new nonempirical generalized gradient approximation (GGA) for density functional theory (DFT) is introduced, which significantly improves the accuracy of lattice constants, crystal structures, and metal surface energies compared to the popular Perdew-Burke-Ernzerhof (PBE) GGA. The new functional is based on a diffuse radial cutoff for the exchange hole in real space and an analytic gradient expansion of the exchange energy for small gradients. It has no adjustable parameters and maintains the constraining conditions of PBE, making it easy to implement in existing codes. The Kohn-Sham DFT allows efficient and accurate calculation of many-electron ground-state problems. However, the exchange-correlation (XC) energy is not known exactly, so approximations are needed. Local density approximation (LDA) and generalized gradient approximations (GGAs) are used, with GGAs improving upon LDA. However, GGAs often overcorrect LDA for solids, leading to inaccurate lattice constants. LSD underestimates the equilibrium lattice constant, while GGAs tend to overestimate it. The new functional addresses these issues by using a diffuse radial cutoff, which results in a smaller exchange enhancement factor $ F_X $ for larger gradients. The new functional, referred to as "WC," is derived from the PBE functional but incorporates a revised form of $ F_X $ that satisfies known constraints and improves accuracy for solids. It performs well for solids, with significant improvements in lattice constants, bulk moduli, and cohesive energies compared to LSD and PBE. For ferroelectrics like $ PbTiO_3 $, WC predicts more accurate volumes and strains than PBE. The new functional also performs better than PBE for jellium surface energies and is more accurate for noble-gas atoms than LSD and PBE. The WC functional is nonempirical, with no adjustable parameters, and is suitable for ab initio calculations of materials requiring high accuracy, such as ferroelectrics. It can be generalized to improve accuracy for atoms, molecules, and solids compared to PBE. The study shows that the accuracy of GGAs depends on the variation of the reduced gradient $ s $ and the density parameter $ r_s $, suggesting that a GGA with $ F_X $ depending on both $ s $ and $ r_s $ could be more accurate than PBE. The new functional represents a significant improvement over existing GGAs and meta-GGAs for solids.