The state of deprotonation/protonation of surfaces has far-ranging implications in chemistry, from acid–base catalysis¹ and the electrocatalytic and photocatalytic splitting of water², to the behaviour of minerals³ and biochemistry⁴. An entity’s acidity is described by its proton affinity and its acid dissociation constant pK_a (the negative logarithm of the equilibrium constant of the proton transfer reaction in solution). The acidity of individual sites is difficult to assess for solids, compared with molecules. For mineral surfaces, the acidity is estimated by semi-empirical concepts, such as bond-order valence sums⁵, and increasingly modelled with first-principles molecular dynamics simulations^6,7. At present, such predictions cannot be tested—experimental measures, such as the point of zero charge⁸, integrate over the whole surface or, in some cases, individual crystal facets⁹. Here we assess the acidity of individual hydroxyl groups on In₂O₃(111)—a model oxide with four different types of surface oxygen atom. We probe the strength of their hydrogen bonds with the tip of a non-contact atomic force microscope and find quantitative agreement with density functional theory calculations. By relating the results to known proton affinities of gas-phase molecules, we determine the proton affinity of the different surface sites of In₂O₃ with atomic precision. Measurements on hydroxylated titanium dioxide and zirconium oxide extend our method to other oxides.

从酸碱催化¹和水的电催化和光催化分解²到矿物的行为³和生物化学⁴ ，表面的去质子化/质子化状态在化学中具有广泛的意义。实体的酸度由其质子亲和力和酸解离常数 p K _a（溶液中质子转移反应的平衡常数的负对数）来描述。与分子相比，固体的单个位点的酸度很难评估。对于矿物表面，酸度是通过半经验概念来估计的，例如键阶化合价和⁵，并且越来越多地使用第一性原理分子动力学模拟^6,7进行建模。目前，这样的预测无法得到检验——实验措施，例如零电荷点⁸，整合在整个表面上，或者在某些情况下，整合到单个晶面⁹上。_{在这里，我们评估了 In 2} O ₃上各个羟基的酸度(111)——具有四种不同表面氧原子的模型氧化物。我们用非接触式原子力显微镜的尖端探测它们的氢键强度，并发现与密度泛函理论计算的定量一致。通过将结果与气相分子的已知质子亲和力联系起来，我们以原子精度确定了 In ₂ O _{3不同表面位点的质子亲和力。}对羟基化二氧化钛和氧化锆的测量将我们的方法扩展到其他氧化物。